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- Q2] As shown in the table below that gives the age distribution of individuals starting new university employments. Find the following probabilities: 1-Ages (28-39). 2- Age>55. 3-Age<35. N:: 3 G: 3 R= 9 Age Frequency 15-24 25-34 35-44 45-54 320-R 420+R 315 55-64 65-74 120 250 220-RS3. Let X₁,..., Xn ~ N(µ, 0²) be independent random variables. What is the distribution of the sum Σ=X;?You are given n observations X1, X2, · · · , Xn that are i.i.d. and follow a geometric distribution with an unknown parameter θ which represents the probability of a success. Find the Maximum Likelihood Estimator of the parameter θ.
- C2. A random variable X is said to follow the discrete uniform distribution on {1,2,... , n} if each value x in that set {1, 2, ... , n} is equally likely. n +1 (a) Show that the expectation of X is EX 2 (b) Find the variance of X. (c) Let Y be a discrete uniform distribution on {a, a + 1, a + 2, ...,b – 1, b}, for integers a and b with a < b. Using parts (a) and (b), but without calculating any sums directly, find the expectation and variance of Y. You may use without proof the standard results п(п + 1) n(n + 1)(2n + 1) n n 2 x=1 x=1 ||Suppose a random variable X following χk2. Describe the distribution of X/k when k is large enough.part D i need in words not handwritten solution
- 8. Be X a discrete random variable with distribution given by: Select one: a. 1/8 b. 1/4 c. 3/8 d. 5/817. Conditional Distributions Consider two random variables X and Y for which we know Pr(X = x) = Pr(X = x|Y = y)for all possible values of x and y. In this case we would say that X and Y are.... Pick ONE option Independent Perfectly correlated Equal to each other More than one of these choices None of these choicesSuppose that X follows a Binomial distribution, i.e., X ∼ Binomial(3, 0.5). Define a new random variable as Y = X 2 , then, what is the value of the PMF of Y evaluated at 1, i.e., what is Pr(Y=1)? a). 0.3125 b). 0.25 c). 0.375 d). 0.5