Joint Probability density finction of randam variables X1 ond X2 16 %3D

calculate the variance of g(X) =X^2+2, where X is the random variable with probability distribution : x=0,1,2,3; f(x) = 0.1, 0.2, 0.4,0.3 . a. 19.65 b. 26.28 c. 10.65 d. 11.65 e. 14.65

Find the probability distribution of the random variable y, which represents the number of times writing appears when a balanced coin is tossed three times. Calculate the mean and variance of the random variable y, whose probability mass function is: f (y) = y^2/30 y = 1,2,3

Let Z be a standard normal random variable. Find formulae for thedensities of |Z|, Z^2, 1/Z, and 1/Z^2

the random variable Y is such that : E(2Y+3)=6    and    Var(2-3Y)=11 find      E(Y^2)

Please do not use ChatGPT,i will be very very appreciate!!Please do not use ChatGPT,i will be very very appreciate!!Please do not use ChatGPT,i will be very very appreciate!!

You are a statistical trainee actuary working for an insurance company. You are part of a statistical modelling team that is developing models based on independent non identically distributed random variables. You consider the following model X; ~ Gamma(awi, B), i= {1,..., N} where a, B, and w1,..,WN are positive scalar parameters (the gamma distribution has several common parametrisations, here we define the p.d.f. of a random variable X ~ as f(x) https://mathworld.wolfram.com/GammaFunction.html). Gamma(a, B) Hora-1 exp{-Bx} for x > 0, where r(-) denotes the gamma function, see You have been asked to explore the statistical properties of the maximum likelihood estimator of B assuming that a and wi,... ,WN are known. Assume that a > 2 andE,wi > 1. Let X = X1,..., XN. You decide to perform the following analyses: 1. State the likelihood function L(B; X) = f(X; B). 2. Derive the maximum likelihood estimator for 3, denoted by B(X). 3. Show that the bias of 3(X) is given by B(B) = B/(a Ewi…

Give me detail pls

Consider a random variable Y with PDF Pr(Y=k)=pq^(k-1),k=1,2,3,4,5....compute for E(2Y)

Let X ~ Uniform(a, b). Find Expected value EX.