B1. Let X be a continuous random variable with PDF 2 f(x) = ½ ½ (2 - x) 9 and f(x) = 0 otherwise. for 1x c (a) Explaining your work, find the value of the constant c. (b) What is P(X > 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X

The CDF F(x) of a random variable X is given by;F(x) = { 0          ,           ?? ? ≤ 1              ? (? − 1)^4   ,  ?? 1 < ? ≤ 3                1           ,         ?? ? > 3} find PDF f(x) (ii) ?(|?| < 1.5), (iii) the mean and variance of X.

f(X)= 3/8( 4x - 2x2 )         0<* x <* 2     (* less or equal to) a.  Find the variance of X.

The discrete random variables X and Y have the following joint probability function Y 0 1 2 1 1/20 2/20 3/20 X 2 2/20 1/20 4/20 3 3/20 1/20 3/20

Show that variance o? = (x²) – ((x))²

Let X and Y be identically distributed with mean 4 and variance 25.(a) If X and Y are uncorrelated, what is the variance of X + Y?(b) If the covariance between X and Y is 8, what is the variance of X + Y? (c) If X and Y are independent, what is E[(X - Y)^2]?

Q6

The random variable Y has the Poisson distribution with a mean of 50. (a) What is the variance of Y? Answer: [Select] (b) Compute the probability, P(Y> 60). Select the closest answer. Answer: [Select] (c) Let Y₁ and Y₂ be two independent observations of Y. What is the variance of (Y₁ + Y₂)? Answer: variance (Y₁ + Y₂) = [Select] (d) Let Y₁ and Y₂ be two independent observations of Y. What is the variance of (Y₁ - Y₂)? Answer: variance (Y₁ - Y₂) = [Select]

pls solve this

C1. Let X be a continuous random variable with PDF f(x) = ? (2 – a) for –1 1)? (c) Calculate the expectation and variance of X. (d) Let Y (X2 – 1). What is the expectation of Y?