Assume that X is a continuous random variable with the following probability density function.
f(x)=3x2
for 0<x<1 Find the probability density function of Y=X2
Assume that X is a continuous random variable with the following probability density function. f(x)=3x2 for...
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
4. Let X be a continuous random variable with probability density function: x<1 0, if if| if x>4 f(x) = (x2 + 1), 4 x 24 0 Find the standard deviation of random variable X.
Let X be a continuous random variable with the following probability density function f 0 < x < 1 otherwise 0 Let Y = 10 X: (give answer to two places past decimal) 1. Find the median (50th percentile) of Y. Submit an answer Tries 0/99 2. Compute p (Y' <1). Submit an answer Tries 0/99 3. Compute E (X). 0.60 Submit an answer Answer Submitted: Your final submission will be graded after the due date. Tries 1/99 Previous attempts...
1. Let X be a continuous random variable with probability density function f(x) = { if x > 2 otherwise 0 Check that f(-x) is indeed a probability density function. Find P(X > 5) and E[X]. 2. Let X be a continuous random variable with probability density function f(x) = = { SE otherwise where c is a constant. Find c, and E[X].
1. (15 points) Let X be a continuous random variable with probability density function f (x) c(1-), 0 < 1, where c is a constant. i) Find the constant c ii) What is the distribution function of X? ii) Let Y 1x<0.5 Find the conditional expectation E(X|Y). 1. (15 points) Let X be a continuous random variable with probability density function f (x) c(1-), 0
A continuous random variable X has the probability density function f(x) = e^(-x), x>0 a) Compute the mean and variance of this random variable. b) Derive the probability density function of the random variable Y = X^3. c) Compute the mean and variance of the random variable Y in part b)
Suppose density function positively valued continuous random variable X has the probability a fx(x)kexp 20 fixed 0> 0 for 0 o0, some k > 0 and for (a) Find k such that f(x) satisfies the conditions for a probability density function (4 marks) (b) Derive expressions for E[X] and Var[X (c) Express the cumulative distribution function Fx(r) in terms of P(), the stan dard Normal cumulative distribution function (8 marks) (8 marks) (al) Derive the probability density function of Y...
b. Let X be a continuous random variable with probability density function f(x) = kx2 if – 1 < x < 2 ) otherwise Find k, and then find P(|X| > 1/2).
2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else The cumulative distribution function is F(x). Find EX.
1. A continuous random variable has probability density function f(x) = 2x for all 0 < x < 1 and f(x) = 0 for all other 2. Find Prli <x< 1. O 1 16 O OP O . O 1