probability interseting question not able to solve it [closed]Probability question.Expected value for...
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probability interseting question not able to solve it [closed]
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$begingroup$
A random variable X can take all non-negative integer values and the probability that $X$ take the value $r$ is proportional to $a^r$ where a is between 0 to 1. Find $Pr{X=0}$
probability
edited Mar 19 at 16:06
Mostafa Ayaz
18.2k31040
asked Mar 19 at 15:52
Shivam Shivam
32
$endgroup$
closed as off-topic by Saad, Lee David Chung Lin, Leucippus, Eevee Trainer, Cesareo Mar 22 at 8:20
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Lee David Chung Lin, Leucippus, Eevee Trainer, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
A random variable X can take all non-negative integer values and the probability that $X$ take the value $r$ is proportional to $a^r$ where a is between 0 to 1. Find $Pr{X=0}$
probability
edited Mar 19 at 16:06
Mostafa Ayaz
18.2k31040
asked Mar 19 at 15:52
Shivam Shivam
32
$endgroup$
closed as off-topic by Saad, Lee David Chung Lin, Leucippus, Eevee Trainer, Cesareo Mar 22 at 8:20
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Lee David Chung Lin, Leucippus, Eevee Trainer, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
A random variable X can take all non-negative integer values and the probability that $X$ take the value $r$ is proportional to $a^r$ where a is between 0 to 1. Find $Pr{X=0}$
probability
edited Mar 19 at 16:06
Mostafa Ayaz
18.2k31040
asked Mar 19 at 15:52
Shivam Shivam
32
$endgroup$
A random variable X can take all non-negative integer values and the probability that $X$ take the value $r$ is proportional to $a^r$ where a is between 0 to 1. Find $Pr{X=0}$
probability
probability
edited Mar 19 at 16:06
Mostafa Ayaz
18.2k31040
asked Mar 19 at 15:52
Shivam Shivam
32
edited Mar 19 at 16:06
Mostafa Ayaz
18.2k31040
asked Mar 19 at 15:52
Shivam Shivam
32
edited Mar 19 at 16:06
Mostafa Ayaz
18.2k31040
edited Mar 19 at 16:06
Mostafa Ayaz
18.2k31040
edited Mar 19 at 16:06
Mostafa Ayaz
18.2k31040
18.2k31040
asked Mar 19 at 15:52
Shivam Shivam
32
asked Mar 19 at 15:52
Shivam Shivam
32
asked Mar 19 at 15:52
Shivam Shivam
32
32
closed as off-topic by Saad, Lee David Chung Lin, Leucippus, Eevee Trainer, Cesareo Mar 22 at 8:20
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Lee David Chung Lin, Leucippus, Eevee Trainer, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Saad, Lee David Chung Lin, Leucippus, Eevee Trainer, Cesareo Mar 22 at 8:20
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Lee David Chung Lin, Leucippus, Eevee Trainer, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The general form of pmf goes like this$$Pr{X=r}=kcdot a^r$$where $k$ is a constant. As any pmf $f(n)$ must satisfy $sum f(n)=1$ we must have $$sum_{r=0}^{infty}Pr{X=r}=sum_{r=0}^{infty}kcdot a^r=ksum_{r=0}^{infty} a^r=1$$therefore $$k={1over sum_{r=0}^{infty} a^r}$$and we need to find $sum_{r=0}^{infty}a^r$ which equals to ${1over 1-a}$ according to geometric series sum formula. Therefore $k=1-a$ and the final answer becomes $$Pr{X=r}={a^rcdot (1-a)}$$so we have$$Pr{X=0}=1-a$$
answered Mar 19 at 16:04
Mostafa AyazMostafa Ayaz
18.2k31040
$endgroup$
$begingroup$
answer again its answer is 1-a
$endgroup$
– Shivam
Mar 19 at 16:06
$begingroup$
thanks great answer
$endgroup$
– Shivam
Mar 19 at 16:20
$begingroup$
Your welcome. Good luck!
$endgroup$
– Mostafa Ayaz
Mar 19 at 16:43
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The general form of pmf goes like this$$Pr{X=r}=kcdot a^r$$where $k$ is a constant. As any pmf $f(n)$ must satisfy $sum f(n)=1$ we must have $$sum_{r=0}^{infty}Pr{X=r}=sum_{r=0}^{infty}kcdot a^r=ksum_{r=0}^{infty} a^r=1$$therefore $$k={1over sum_{r=0}^{infty} a^r}$$and we need to find $sum_{r=0}^{infty}a^r$ which equals to ${1over 1-a}$ according to geometric series sum formula. Therefore $k=1-a$ and the final answer becomes $$Pr{X=r}={a^rcdot (1-a)}$$so we have$$Pr{X=0}=1-a$$
answered Mar 19 at 16:04
Mostafa AyazMostafa Ayaz
18.2k31040
$endgroup$
$begingroup$
answer again its answer is 1-a
$endgroup$
– Shivam
Mar 19 at 16:06
$begingroup$
thanks great answer
$endgroup$
– Shivam
Mar 19 at 16:20
$begingroup$
Your welcome. Good luck!
$endgroup$
– Mostafa Ayaz
Mar 19 at 16:43
add a comment |
$begingroup$
The general form of pmf goes like this$$Pr{X=r}=kcdot a^r$$where $k$ is a constant. As any pmf $f(n)$ must satisfy $sum f(n)=1$ we must have $$sum_{r=0}^{infty}Pr{X=r}=sum_{r=0}^{infty}kcdot a^r=ksum_{r=0}^{infty} a^r=1$$therefore $$k={1over sum_{r=0}^{infty} a^r}$$and we need to find $sum_{r=0}^{infty}a^r$ which equals to ${1over 1-a}$ according to geometric series sum formula. Therefore $k=1-a$ and the final answer becomes $$Pr{X=r}={a^rcdot (1-a)}$$so we have$$Pr{X=0}=1-a$$
answered Mar 19 at 16:04
Mostafa AyazMostafa Ayaz
18.2k31040
$endgroup$
$begingroup$
answer again its answer is 1-a
$endgroup$
– Shivam
Mar 19 at 16:06
$begingroup$
thanks great answer
$endgroup$
– Shivam
Mar 19 at 16:20
$begingroup$
Your welcome. Good luck!
$endgroup$
– Mostafa Ayaz
Mar 19 at 16:43
add a comment |
$begingroup$
The general form of pmf goes like this$$Pr{X=r}=kcdot a^r$$where $k$ is a constant. As any pmf $f(n)$ must satisfy $sum f(n)=1$ we must have $$sum_{r=0}^{infty}Pr{X=r}=sum_{r=0}^{infty}kcdot a^r=ksum_{r=0}^{infty} a^r=1$$therefore $$k={1over sum_{r=0}^{infty} a^r}$$and we need to find $sum_{r=0}^{infty}a^r$ which equals to ${1over 1-a}$ according to geometric series sum formula. Therefore $k=1-a$ and the final answer becomes $$Pr{X=r}={a^rcdot (1-a)}$$so we have$$Pr{X=0}=1-a$$
answered Mar 19 at 16:04
Mostafa AyazMostafa Ayaz
18.2k31040
$endgroup$
The general form of pmf goes like this$$Pr{X=r}=kcdot a^r$$where $k$ is a constant. As any pmf $f(n)$ must satisfy $sum f(n)=1$ we must have $$sum_{r=0}^{infty}Pr{X=r}=sum_{r=0}^{infty}kcdot a^r=ksum_{r=0}^{infty} a^r=1$$therefore $$k={1over sum_{r=0}^{infty} a^r}$$and we need to find $sum_{r=0}^{infty}a^r$ which equals to ${1over 1-a}$ according to geometric series sum formula. Therefore $k=1-a$ and the final answer becomes $$Pr{X=r}={a^rcdot (1-a)}$$so we have$$Pr{X=0}=1-a$$
answered Mar 19 at 16:04
Mostafa AyazMostafa Ayaz
18.2k31040
edited Mar 19 at 16:10
answered Mar 19 at 16:04
Mostafa AyazMostafa Ayaz
18.2k31040
answered Mar 19 at 16:04
Mostafa AyazMostafa Ayaz
18.2k31040
answered Mar 19 at 16:04
Mostafa AyazMostafa Ayaz
18.2k31040
18.2k31040
$begingroup$
answer again its answer is 1-a
$endgroup$
– Shivam
Mar 19 at 16:06
$begingroup$
thanks great answer
$endgroup$
– Shivam
Mar 19 at 16:20
$begingroup$
Your welcome. Good luck!
$endgroup$
– Mostafa Ayaz
Mar 19 at 16:43
add a comment |
$begingroup$
answer again its answer is 1-a
$endgroup$
– Shivam
Mar 19 at 16:06
$begingroup$
thanks great answer
$endgroup$
– Shivam
Mar 19 at 16:20
$begingroup$
Your welcome. Good luck!
$endgroup$
– Mostafa Ayaz
Mar 19 at 16:43
$begingroup$
answer again its answer is 1-a
$endgroup$
– Shivam
Mar 19 at 16:06
$begingroup$
answer again its answer is 1-a
$endgroup$
– Shivam
Mar 19 at 16:06
$begingroup$
thanks great answer
$endgroup$
– Shivam
Mar 19 at 16:20
$begingroup$
thanks great answer
$endgroup$
– Shivam
Mar 19 at 16:20
$begingroup$
Your welcome. Good luck!
$endgroup$
– Mostafa Ayaz
Mar 19 at 16:43
$begingroup$
Your welcome. Good luck!
$endgroup$
– Mostafa Ayaz
Mar 19 at 16:43
add a comment |
