Thread: Cumulative distribution function probs

Let random variable X have the cdf F given by:

F(x)= { 0 for x ≤ 0
(x^3/8) for 0< x<2
1 for x ≥ 2


1. Find P(X ≤ 2/3)

[(2/3)^3]/8 = .37



2. Find the probability density function for X

f(x) = x^2/16


3. Let random Variable Y = F(X). Find the Probability P(Y ≤ 2/3)



I just want to check my answers for parts 1 and 2. Can someone please help me with part 3

Originally Posted by plm2e

Let random variable X have the cdf F given by:

F(x)= { 0 for x ≤ 0
(x^3/8) for 0< x<2
1 for x ≥ 2


1. Find P(X ≤ 2/3)

[(2/3)^3]/8 = .37



2. Find the probability density function for X

f(x) = x^2/16


3. Let random Variable Y = F(X). Find the Probability P(Y ≤ 2/3)



I just want to check my answers for parts 1 and 2. Can someone please help me with part 3

1. [(2/3)^3]/8: Correct. 0.37: Wrong.

2. f(x) = dF/dx. You have not differentiated correctly.