Continuous Random Variable X, Find pdf of Y when Y = √X. Part d. [closed]
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A continuous random variable X has the following probability density function:
k(x+x3), 0≤x≤2 f(x) = 0, otherwise
(a) Find the value of k
(b) Find the mean and variance of X,
(c) Find P(X ≤ 1).
(d) If Y =√X, determine the probability density function for Y, and hence, or otherwise, find the mean and variance for Y.
I am struggling with part d. I am not sure what to do as this is a non-linear relationship between X and Y.
probability-theory probability-distributions problem-solving
asked Nov 23 at 17:27
J Borland
11
closed as off-topic by José Carlos Santos, NCh, amWhy, Shailesh, John B Dec 1 at 0:44
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, NCh, amWhy, Shailesh, John B
If this question can be reworded to fit the rules in the help center, please edit the question.
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up vote
-1
down vote
favorite
A continuous random variable X has the following probability density function:
k(x+x3), 0≤x≤2 f(x) = 0, otherwise
(a) Find the value of k
(b) Find the mean and variance of X,
(c) Find P(X ≤ 1).
(d) If Y =√X, determine the probability density function for Y, and hence, or otherwise, find the mean and variance for Y.
I am struggling with part d. I am not sure what to do as this is a non-linear relationship between X and Y.
probability-theory probability-distributions problem-solving
asked Nov 23 at 17:27
J Borland
11
closed as off-topic by José Carlos Santos, NCh, amWhy, Shailesh, John B Dec 1 at 0:44
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, NCh, amWhy, Shailesh, John B
If this question can be reworded to fit the rules in the help center, please edit the question.
refer math.meta.stackexchange.com/questions/5020/… for proper mathjax formatting
– idea
Nov 23 at 18:16
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up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
A continuous random variable X has the following probability density function:
k(x+x3), 0≤x≤2 f(x) = 0, otherwise
(a) Find the value of k
(b) Find the mean and variance of X,
(c) Find P(X ≤ 1).
(d) If Y =√X, determine the probability density function for Y, and hence, or otherwise, find the mean and variance for Y.
I am struggling with part d. I am not sure what to do as this is a non-linear relationship between X and Y.
probability-theory probability-distributions problem-solving
asked Nov 23 at 17:27
J Borland
11
A continuous random variable X has the following probability density function:
k(x+x3), 0≤x≤2 f(x) = 0, otherwise
(a) Find the value of k
(b) Find the mean and variance of X,
(c) Find P(X ≤ 1).
(d) If Y =√X, determine the probability density function for Y, and hence, or otherwise, find the mean and variance for Y.
I am struggling with part d. I am not sure what to do as this is a non-linear relationship between X and Y.
probability-theory probability-distributions problem-solving
probability-theory probability-distributions problem-solving
asked Nov 23 at 17:27
J Borland
11
asked Nov 23 at 17:27
J Borland
11
asked Nov 23 at 17:27
J Borland
11
asked Nov 23 at 17:27
J Borland
11
asked Nov 23 at 17:27
J Borland
11
11
closed as off-topic by José Carlos Santos, NCh, amWhy, Shailesh, John B Dec 1 at 0:44
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, NCh, amWhy, Shailesh, John B
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by José Carlos Santos, NCh, amWhy, Shailesh, John B Dec 1 at 0:44
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, NCh, amWhy, Shailesh, John B
If this question can be reworded to fit the rules in the help center, please edit the question.
refer math.meta.stackexchange.com/questions/5020/… for proper mathjax formatting
– idea
Nov 23 at 18:16
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refer math.meta.stackexchange.com/questions/5020/… for proper mathjax formatting
– idea
Nov 23 at 18:16
refer math.meta.stackexchange.com/questions/5020/… for proper mathjax formatting
– idea
Nov 23 at 18:16
refer math.meta.stackexchange.com/questions/5020/… for proper mathjax formatting
– idea
Nov 23 at 18:16
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2 Answers
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For (d) $F_Y(y)=P(Yle y)=P(sqrt{X}le y)=P(Xle y^2)={kint_0^{y^2}(x+x^3)dx=k(frac{y^4}{2}+frac{y^8}{4})}$
The density function $f_Y(y)=k(2y^3+2y^7)$, for $0le ylesqrt{2}$.
I'll leave the mean and variance calculation to you.
answered Nov 23 at 18:37
herb steinberg
2,2932310
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We have $$Pr(Y<y)=Pr{(sqrt X<y)}=Pr(X<y^2)=F_X(y^2)$$therefore$$f_Y(y)=2yf_X(y^2)$$
answered Nov 23 at 18:56
Mostafa Ayaz
13.3k3836
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
For (d) $F_Y(y)=P(Yle y)=P(sqrt{X}le y)=P(Xle y^2)={kint_0^{y^2}(x+x^3)dx=k(frac{y^4}{2}+frac{y^8}{4})}$
The density function $f_Y(y)=k(2y^3+2y^7)$, for $0le ylesqrt{2}$.
I'll leave the mean and variance calculation to you.
answered Nov 23 at 18:37
herb steinberg
2,2932310
add a comment |
up vote
0
down vote
For (d) $F_Y(y)=P(Yle y)=P(sqrt{X}le y)=P(Xle y^2)={kint_0^{y^2}(x+x^3)dx=k(frac{y^4}{2}+frac{y^8}{4})}$
The density function $f_Y(y)=k(2y^3+2y^7)$, for $0le ylesqrt{2}$.
I'll leave the mean and variance calculation to you.
answered Nov 23 at 18:37
herb steinberg
2,2932310
add a comment |
up vote
0
down vote
up vote
0
down vote
For (d) $F_Y(y)=P(Yle y)=P(sqrt{X}le y)=P(Xle y^2)={kint_0^{y^2}(x+x^3)dx=k(frac{y^4}{2}+frac{y^8}{4})}$
The density function $f_Y(y)=k(2y^3+2y^7)$, for $0le ylesqrt{2}$.
I'll leave the mean and variance calculation to you.
answered Nov 23 at 18:37
herb steinberg
2,2932310
For (d) $F_Y(y)=P(Yle y)=P(sqrt{X}le y)=P(Xle y^2)={kint_0^{y^2}(x+x^3)dx=k(frac{y^4}{2}+frac{y^8}{4})}$
The density function $f_Y(y)=k(2y^3+2y^7)$, for $0le ylesqrt{2}$.
I'll leave the mean and variance calculation to you.
answered Nov 23 at 18:37
herb steinberg
2,2932310
answered Nov 23 at 18:37
herb steinberg
2,2932310
answered Nov 23 at 18:37
herb steinberg
2,2932310
answered Nov 23 at 18:37
herb steinberg
2,2932310
2,2932310
add a comment |
add a comment |
up vote
0
down vote
We have $$Pr(Y<y)=Pr{(sqrt X<y)}=Pr(X<y^2)=F_X(y^2)$$therefore$$f_Y(y)=2yf_X(y^2)$$
answered Nov 23 at 18:56
Mostafa Ayaz
13.3k3836
add a comment |
up vote
0
down vote
We have $$Pr(Y<y)=Pr{(sqrt X<y)}=Pr(X<y^2)=F_X(y^2)$$therefore$$f_Y(y)=2yf_X(y^2)$$
answered Nov 23 at 18:56
Mostafa Ayaz
13.3k3836
add a comment |
up vote
0
down vote
up vote
0
down vote
We have $$Pr(Y<y)=Pr{(sqrt X<y)}=Pr(X<y^2)=F_X(y^2)$$therefore$$f_Y(y)=2yf_X(y^2)$$
answered Nov 23 at 18:56
Mostafa Ayaz
13.3k3836
We have $$Pr(Y<y)=Pr{(sqrt X<y)}=Pr(X<y^2)=F_X(y^2)$$therefore$$f_Y(y)=2yf_X(y^2)$$
answered Nov 23 at 18:56
Mostafa Ayaz
13.3k3836
answered Nov 23 at 18:56
Mostafa Ayaz
13.3k3836
answered Nov 23 at 18:56
Mostafa Ayaz
13.3k3836
answered Nov 23 at 18:56
Mostafa Ayaz
13.3k3836
13.3k3836
add a comment |
add a comment |
refer math.meta.stackexchange.com/questions/5020/… for proper mathjax formatting
– idea
Nov 23 at 18:16