Problem 3. The probability density function of X is f(x)o otherwise where k is some positive...
Problem(2) (5 points) A continuous distribution has density function k sin(r); 0rST 0; f(x) = otherwise. (a) Find the numerical value of k so that f(r) is a density function. (b) Find E[X] (c) Find E[X2. (d) Find Var X] Problem(2) (5 points) A continuous distribution has density function k sin(r); 0rST 0; f(x) = otherwise. (a) Find the numerical value of k so that f(r) is a density function. (b) Find E[X] (c) Find E[X2. (d) Find Var X]
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
5. Find the moment generating function of the continuous random variable X whose a. probability density is given by )-3 or 36 0 elsewhere find the values of μ and σ2. b, Let X have an exponential distribution with a mean of θ = 15 . Compute a. 6. P(10 < X <20); b. P(X>20), c. P(X>30X > 10), the variance and the moment generating function of x. d.
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...
(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.
Please do not copy, all the previous answers are wrong. 3. The joint probability density function of X and Y is given by 2 if O< x S 2,0 < y, and x +ys1 otherwise f(x,y) = 〉cry (a) Determine the value of c (b) Find the marginal probability density function of X and Y (c) Compute Cov(X, Y) (d) Compute Var(X2 Y) (e) Determine if X and Y are independent. 3. The joint probability density function of X and...
A continuous random variable X has probability density function f(x) = a for −2 < x < 0 bx for 0 < x ≤ 1 0 otherwise where a and b are constants. It is known that E(X) = 0. (a) Determine a and b. (b) Find Var(X) (c) Find the median of X, i.e. a number m such that P(X ≤ m) = 1/2
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...
The random variable X has probability density function k(x25x-4) 1<x<4 otherwise -{ f(x) 1. Show thatk. (5pts) Find 2. Е (X), (5pts) 3. the mode of X, (5pts) 4. the cumulative distribution function F(X) for all x. (5pts) 5. Evaluate P(X < 2.5). (5pts) 6. Deduce the value of the median and comment on the shape of the distribution (10pts)