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

Let X have a mean of 132 and a variance of 32. Define Y = X² + 2X + 1. Compute the (a) mean and (b) variance of Y. (a) i (b) i

(b) Find the variance Var(X) of X.

The intensity of a hurricane is a random variable that is uniformly distributed on the interval [0, 3]. The damage from a hurricane with a given intensity y is exponentially distributed with a mean equal to y. Calculate the variance of the damage from a random hurricane. (A) 1.73 (B) 1.94 (C) 3.00 (D) 3.75 (E) 6.00

Let X be a random variable with mean E[X] = 20 and variance Var(X) = 3. Define Y = 3 – 6X. Calculate the mean and variance of Y.

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.

Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the variance of X.

Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.

Show that variance o? = (x²) – ((x))²