Let Z be a standard normal random variable. Find formulae for the densities of |Z|, Z^2, 1/Z, and 1/Z^2
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Let Z be a standard normal random variable. Find formulae for the
densities of |Z|, Z^2, 1/Z, and 1/Z^2
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- X is normally distributed with mean 2 and standard deviation 3. Y is normally distributed with mean 4 and standard deviation 4. What is P(Y > X)? (a) If X and Y are independent? (b) If X, Y have a multivariate normal distribution, and Cov(X, Y ) = 2?A standard normal variable Z can be transformed to the normally distributed random variable X with only mean µ known. True or FalseWhich is not an assumed characteristic of & in the population model y₁ = Be + B₁ X₁ + εi? Multiple Choice It is a random variable. It has zero mean. ○ It is a statistic. It is unobservable.
- Let X = ((X1,Y1),...,(X, Yn)) be a sample from a bivariate normal population. Show that the distributions of X form a five-parameter exponential family and identify п, В, Г, and h.According to the empirical (68-95-99.7) rule, if a random variable z has a standard normal distribution, then approximately 95% of all values fall between z-scores of -2 and 2. Use the standard normal table or software to determine the precise positive value of z such that 95% of the area under the standard normal density curve is between -z and z. If you use software, you may find this list of manuals useful. Give the positive value of z precise to two decimal places.Let X be a normal random variable with mean μ=10 and variance σ^2=36. Find (a)P{X<22} (b)P{X>5} (c)P{4<X<16}
- Let X be a strictly positive random variable. Determine which of the following quantitiesare larger:(a) E(X^4) or (E(X))^4(b) E(X^1/9) or (E(X))^1/9(c) E(X^3 + 4X^2 + 9) or (E(X))^3 + 4(E(X))^2 + 9(d) E(e^X ) or e^E(X)(e) E(arctan(X)) or arctan(E(X))Solve (F,G,H,i) only Please!!!We have a random variable X that is uniformly distributed on interval [-1,2]. Let Y = |X| - 1. We want to find pdf using CDF technique. What is the support and pdf for the random variable Y? What would fy(-.2) be? What about Fy(-.2) be?
- The random variable X ( N (u,5^2)and P(X < 23)= 0.9192. (a) Find the value of u . (b) Find the value of P(u< X < 23).Identify the distributions of the random variables with the moment- generating functions shown below. For each random variable also indicate what the mean and the variance are. a) m(t) = e^2.2(e^t−1)b) m(t) = 1/(1 − 2t)^2 c) m(t) =( e^5t−e^t )/4tThe useful life of a concrete built on the seashore has a Weibull distribution of parameter scale δ> 0 year and power β = 2. Determine a) The half life of concrete EXb) The variance VXc) The probability that the concrete lasts more than 10 years; P (X> 10)
