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Consider the probability density function 0 ifr <0 8.77 if 0 < x <1 0 if...
7. For the probability density function f(x) = for 0 <<<2 (a) Find P(x < 1) (b) Find the expected value. (c) Find the variance.
The probability density function of X is given by 0 elsewhere Find the probability density function of Y = X3 f(r)-(62(1-x)for0 < x < 1
3,40 A random variable X has probability density function fx(x) = 1 0<x< 1. Find the probability density function of Y = 4x3 - 2.
If the probability density function of X is given by n2 for 1<x< 2 fx ) = 10 elsewhere (a) Find, E[X], E[X2], and E[X3] (b) Use your answer to part (a) to find E[X3 + 3X2 - 2x + 5)
1. Consider the joint probability density function 0<x<y, 0<y<1, fx.x(x, y) = 0, otherwise. (a) Find the marginal probability density function of Y and identify its distribution. (5 marks (b) Find the conditional probability density function of X given Y=y and hence find the mean and variance of X conditional on Y=y. [7 marks] (c) Use iterated expectation to find the expected value of X [5 marks (d) Use E(XY) and var(XY) from (b) above to find the variance of...
6. For the probability density function given by +1) -1<x<1, compute, using the definition the mean and variance of the distribution.
stats (6) Consider the following joint probability density function of the random variables X and f(x,y) = 9, 1<x<3, 1<y< 2, elsewhere. (a) Find the marginal density functions of X and Y. (b) Are X and Y independent? (c) Find P(X > 2).
Question 13 The cumulative distribution function of X is given by Fx (x) = {-kr <0 0<x<2 > 2 Find (a) the value of k, (b) the probability density function fx (x), (c) the median of X, (d) the variance of X.
2. Let X have probability density function JX2) = 1/2 0<x< 1 3 < x < 4 otherwise Find the cumulative distribution function of X.
6. Let X be a continuous random variable whose probability density function is: 0, x <0, x20.5 Find the median un the mode. 7. Let X be a continuous random variable whose cumulative distribution function is: F(x) = 0.1x, ja 0S$s10, Find 1) the densitv function of random variable U-12-X. 0, ja x<0, I, ja x>10.