Problem 2: Let X be a continuous random variable with the followi probability density function S3a², for æ € [0, 1] 0 otherwise f(x) = • Compute E[X] and Var(X) • Compute P[0.25 < X < 0.75]
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PDF of X is given by,
So,
Now,
We know,
Var(X)
= E(X2) - E(X)2
=0.6 - 0.752
=0.0375
=
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- Suppose a random variable X has a probability density function given by O elsewhere f (x) = kx (1 − x) 0 ≤ x ≤ 1 0 elsewhere a. Find the value of k that makes this a probability density function b. Find P (0.4 ≤ x ≤ 1) c. Find P(x ≤ 0.4) d. Find P (0.8 ≤ x))Suppose that X is a continuous random variable with a probability density function is given by f(x)= 25 when x is between -2 and 2, and f(x)=0 otherwise. a.)Find E(X2), where X is raised to the power 2 b.) Find Var(2X+2)1. Which of the following is FALSE for a continuous random variable X with pdf y = f(x)? %3D A. P(6 S XS 9) = P(6 < X< 9) B. P(6 s XS 9) = f(6)+f(7)+f(8)+f(9) %3D C. P(6 < XS9) = area under the curve y=f(x) between 6 and 9 D. P(X = 9) = 0
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