2. The probability density function of X is given by 10 0,x < 10 a) Find...
2. Let X have probability density function JX2) = 1/2 0<x< 1 3 < x < 4 otherwise Find the cumulative distribution function of X.
2. A random variable has a probability density function given by: Bmx-(B+1) x20 x<m fx(x)= 10 where m>0 and B > 2. Let m and ß be constants; answer the questions in terms of m and B. (a) Find the cumulative distribution function (cdf) Fx(x) of this random variable; (b) Find the mean of X; (c) Find E[X']; and (d) Find the variance of X. [12 points]
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.
Suppose a joint probability density function for two variables X and Y is given as follows: {24x0, if 0 < x < 1,0 < y < 1 f(x, y) = otherwise Please find the probability p (w > 1) =? 3
Show steps, thanks! 2.5.9. The random variable X has a cumulative distribution function 0, forx<0 F(x) for x > 0. for x > , 1+x2" · Find the probability density function of X.
(1) Suppose that X is a continuous random variable with probability density function 0<x< 1 f() = (3-X)/4 i<< <3 10 otherwise (a) Compute the mean and variance of X. (b) Compute P(X <3/2). (c) Find the first quartile (25th percentile) for the distribution.
4. Consider the probability density function (x)for x>0, and zero otherwise. Determine a. The value of a b. P(X> 22) C. e The value of x such that P(X<x)-0.1
Q1: Suppose the probability density function of the magnitude X of a bridge (in newtons) is given by fx)-[e(1+3) sxs2 otherwise (a) Find the value of c. (b) Find the mean and variance (c) Find P(1 <x<2.25) (d) Find the cumulative distribution function.
A mixed random variable X has the cumulative distribution function e+1 (a) Find the probability density function. (b) Find P(0< X < 1).
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.