A random variable X has the density function f(x) = c/(x2+1)
where (a) Find the value of the constant c. (b) Find the probability that X2 lies between 1/3 and 1.

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help! Find the expectation of a discrete random variable X whose probability function is given by f(x) = (1/2)x x=1,2,3,...
EXERCISE (x2+1), where . < 1) A random variable X has the density function f(x)= a) Find the value of the constant C b) Find the probability that X lies between 1/3 and 1
7. Let X a be random variable with probability density function given by -1 < x < 1 fx(x) otherwise (a) Find the mean u and variance o2 of X (b) Derive the moment generating function of X and state the values for which it is defined (c) For the value(s) at which the moment generating function found in part (b) is (are) not defined, what should the moment generating function be defined as? Justify your answer (d) Let X1,...
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].
Find mean and variance of a random variable whose probability density function is given by f(x) = C(x + 1) when -1<= x <=1 otherwise f(x) = 0 Find C values also.
Suppose the random variable X has probability density function (pdf) - { -1 < x<1 otherwise C fx (x) C0 : where c is a constant. (a) Show that c = 1/7; (b) Graph fx (х); (c) Given that all of the moments exist, why are all the odd moments of X zero? (d) What is the median of the distribution of X? (e) Find E (X2) and hence var X; (f) Let X1, fx (x) What is the limiting...
Suppose that a random variable X has a probability density function given by f(x) = kx(1-x)^2 for 0 <x <1 Find the value of k that makes this a probability density function.
help
a random variable X has density function f(x) = cx2 for 0<x<3 and f(x)= 0 others. a. Find constant value o b. Find probability P(1 < X < 2)
Find the mean and variance of the random variable X with
probability function or density f(x)
f(x) = k(1 – x2) if –1 3x = 1 and 0 otherwise
Let X be a random variable with probability density function
a) Find the mean of X
b) Find the standard deviation of X round to four
decimal places.
c) Let G = X2 Find the probability
density function fG of G
Show work for each part plz
f(x) = { 1 x (3-X) it osx=2 Co otherwise
The probability density function of a continuous random variable X is given as shown. I f(x) a) (7.5 pts) Find the value of the constant k as a fraction. b) (7.5 pts) Find the probability P(1sx53). c) (5 pts) Find the value of x such that P(Xsx)=0.5.