**Calculate the Mean Value (Expected Value) of the Following Discrete Variable x:** - \( x = 0, 1, 2, 3, 4, 5, 6 \) - \( p(x) = 0.2, 0.2, 0.15, 0.15, 0.15, 0.1, 0.05 \) To find the mean value (expected value) of a discrete random variable, use the formula: \[ E(X) = \sum [x \times p(x)] \] where \( x \) represents the value of the discrete random variable and \( p(x) \) represents the probability of each value. Calculate by multiplying each \( x \) value by its corresponding probability, and then summing these products.

X is the number of successes in 10 independent Bernoulli trials. The variance of X is equal to 3/4 of the expectation of X (ie Var(X)=0.75E(X)). The probability that X is less than 2 is equal to_____. Please fill in the blank.

Q.7 For an exponential distribution fx(x; p) = (ue H, x20 %3D e. w. where u > 0 Write (Don't derive) (a) Mean (expected value), i.e. E(X). (b) Standard deviation, i.e. S.D. (X). (c) Moment generating function, i.e. Mx(t). (d) Cumulative distribution function (cdf), Fx(x). of Nizv

The two assets, X and Y, whose returns are shown in the multivariate distribution to the right, have the following expected returns, variances, covariance, and correlation: mX = 13.00%; mY = 12.50%; sX = 3.317%; sY = 2.500%; Cov(X,Y) = -.0004; rXY = -.45 a) What is the expected return and standard deviation of a portfolio that is 50% Asset X and 50% Asset Y? b) What is the expected return and standard deviation of a portfolio that is 75% Asset X and 25% Asset Y? c) Which of the preceding portfolios ((a) or (b)) is better? Why?   show all work and formulas used in excel