Suppose that the density function of a continuous random variable is given by f(x)=c(e-2x-e-3x) for non-negative...
22. Given a continuous random variable X with probability density function f(x) = {2x, if :05451 otherwise a. Find P(0.3< X< 0.6) b. Find the mean of X C. Find the standard deviation of X.
9.) Suppose that X is a continuous random variable with density C(1- if [0,1] px(x) ¡f x < 0 or x > 1. (a) Find C so that px is a probability density function. (b) Find the cumulative distribution of X (c) Calculate the probability that X є (0.1,0.9). (d) Calculate the mean and the variance of 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.
9.) Suppose that X is a continuous random variable with density C(1- if r [0,1 0 ¡f x < 0 or x > 1. (a) Find C so that px is a probability density function (b) Find the cumulative distribution of X (c) Calculate the probability that X є (0.1,0.9). (d) Calculate the mean and the variance of X 10.) Suppose that X is a continuous random variable with cumulative distribution function Fx()- arctan()+ (a) Find the probability density function...
Let X be a continuous random variable whose probability density function is fax) (2x +af (0 1) if x E (0; 1) f (x) - ind 1) the coefficient a; 2) P(0.5<X<0.7); 3) P(X 3) Part 3 sample of measurements is given XI-8 -210|2|8 Y 8 4 2 2 0
Suppose that X is a continuous random variable with density
pX(x) = ( Cx(1 − x) if x ∈ [0, 1] 0 if x < 0 or x > 1.
(a) Find C so that pX is a probability density function.
(b) Find the cumulative distribution of X.
(c) Calculate the probability that X ∈ (0.1, 0.9).
(d) Calculate the mean and the variance of X.
9.) Suppose that X is a continuous random variable with density C(1x) if E...
Given that the random variable X has density function 7. 2x, 0<x <a f(a)-t o, otherwise a) Determine a. Find. P (2 < X < 4) and P (-2 < X < 2 b) Determine the parameter A in PDF given by the formula: f(x) -AeAt. Calculate the probabilities given in the above intervals of x
Given that the random variable X has density function 7. 2x, 0
Suppose that X is a continuous random variable whose probability density function is given by (C(4x sa f(x) - 0 otherwise a) What is the value of C? b) Find PX> 1)
The probability density function of a continuous random variable is given by otherwisexc x xf x03 2 30.2 0 2( )Find:a) the value of c.b) E(x)c) E(7 2x)
(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.