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2. Le X be a continuous random variable with the probability density function x+2 18 -2<x<4,...
2. Le X be a continuous random variable with the probability density function x+2 -2<x<4, zero...
2. Le X be a continuous random variable with the probability density function x+2 -2<x<4, zero otherwise. = , Find the probability distribution of Y-g(x)- 12 XI
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given...
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)
b. Let X be a continuous random variable with probability density function f(x) = kx2 if...
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).
4. Let X be a continuous random variable with probability density function: x<1 0, if if|...
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.
1. Let X be a continuous random variable with probability density function f(x) = { if...
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].
Q 2. The probability density function of the continuous random variable X is given by Shell,...
Q 2. The probability density function of the continuous random variable X is given by Shell, -<< 0. elsewhere. f(x) = {&e*, -40<3<20 (a) Derive the moment generating function of the continuous random variable X. (b) Use the moment generating function in (a) to find the mean and variance of X.
2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else...
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.
5. (28 points) A continuous random variable X has probability density function given by f(x) = 3x^2,0<x< 1 O...
5. (28 points) A continuous random variable X has probability density function given by f(x) = 3x^2,0<x< 1 O otherwise (c) What is the c.d.f. of Y = X^2 - 1? What is the p.d.f. of Y = X^2 - 1?
Suppose that X is a continuous random variable with probability distribution Suppose that X is a...
Suppose that X is a continuous random variable with probability
distribution
Suppose that X is a continuous random variable with probability distribution O<x<6 18 (a) Find the probability distribution of the random variable Y-10X 3. fr o) 2 Edit for Sy s (b) Find the expected value of Y
3) The continuous random variable X has the probability density function, ), 2 3x3 f(x) =...
3) The continuous random variable X has the probability density function, ), 2 3x3 f(x) = { a, 35x55 2 - bx, 5 < x < 6 elsewere 10 i)Find the value of a and b and hence, sketch f(x) ii) Find the cumulative distribution function, f(x) and sketch it.
2. Le X be a continuous random variable with the probability density function x+2 -2<x<4, zero otherwise. = , Find the probability distribution of Y-g(x)- 12 XI
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)
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).
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.
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].
Q 2. The probability density function of the continuous random variable X is given by Shell, -<< 0. elsewhere. f(x) = {&e*, -40<3<20 (a) Derive the moment generating function of the continuous random variable X. (b) Use the moment generating function in (a) to find the mean and variance of X.
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.
5. (28 points) A continuous random variable X has probability density function given by f(x) = 3x^2,0<x< 1 O otherwise (c) What is the c.d.f. of Y = X^2 - 1? What is the p.d.f. of Y = X^2 - 1?
Suppose that X is a continuous random variable with probability
distribution
Suppose that X is a continuous random variable with probability distribution O<x<6 18 (a) Find the probability distribution of the random variable Y-10X 3. fr o) 2 Edit for Sy s (b) Find the expected value of Y
3) The continuous random variable X has the probability density function, ), 2 3x3 f(x) = { a, 35x55 2 - bx, 5 < x < 6 elsewere 10 i)Find the value of a and b and hence, sketch f(x) ii) Find the cumulative distribution function, f(x) and sketch it.
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