Given the probability distributions for variables X and Y shown to the​ right, compute the terms below.

If X and Y are two random variables, then which of the following is WRONG?

uppose Company 1’s simple return X is a random variable and takes three possiblevalues {−0.1, 0.1, 0.2}. Company 2’s simple return Y is a random variable and takes twopossible values {−0.3, 0.4}. The joint probability distribution f (X, Y ) is as follows:f (X = −0.1, Y = −0.3) = 0.2, f (X = 0.1, Y = −0.3) = 0.2, f (X = 0.2, Y = −0.3) = 0.1,f (X = −0.1, Y = 0.4) = 0.1, f (X = 0.1, Y = 0.4) = 0.2, f (X = 0.2, Y = 0.4) = 0.2Please calculate the following:(a). Marginal distributions: fX (x) and fY (y);(b). Mean: E[X] and E[Y ];(c). Variance: var(X) and var(Y );(d). Covariance: cov(X, Y );(e). Correlation: corr(X, Y )

Random variable X may take value -1 or 1; Y may take value 1, 2 or 3. The following Table shows the joint probability of random variables X and Y.Y1 2 3X -1 0.1 0.2 0.31 0.2 0.1 0.1Table 2: Joint probability distribution of X and Y. For example, the probability of X=-1 and Y=1 is 0.1. Provide solution to all questions below.(a) Marginal probability distribution of X(b) The expected value, variance and standard deviation of X. (c) Marginal probability distribution of Y(d) The expected value, variance and standard deviation of Y. (e) Conditional probability distribution of Y given X=-1.(f) The conditional expected value, conditional variance and conditional standard deviation of Y

. The two-dimensional random variables ( 𝑋 , 𝑌 ) (X,Y) have the joint density function: 𝑓 ( 𝑥 , 𝑦 ) = 2 𝑥 + 𝑦 20 , 𝑥 = 0 , 1 , 2 ,  and  𝑦 = 0 , 1 , 2 f(x,y)= 20 2x+y ​ ,x=0,1,2, and y=0,1,2 (a) Find the joint cumulative distribution function (CDF) of 𝑋 X and 𝑌 Y. (b) Determine if 𝑋 X and 𝑌 Y are independent.

Let 𝑋∼Bernoulli(0.4)X∼Bernoulli(0.4) and 𝑌∼Bernoulli(0.8)Y∼Bernoulli(0.8) be independent. Define 𝑍=𝑋+𝑌−𝑋𝑌Z=X+Y−XY, find the distribution of 𝑍Z.Bernoulli(0.88)Bernoulli(0.88)Bernoulli(0.12)Bernoulli(0.12)Bernoulli(0.92)Bernoulli(0.92)Bernoulli(0.08)Bernoulli(0.08)