If A1,…,An are Bernoulli random variables with parameter 0.4 and E[A1+...+An]=8.4, then what is n?
If A1,…,An are Bernoulli random variables with parameter 0.4 and E[A1+...+An]=8.4, then what is n?
5. Let Xi, , X, (n 3) be iid Bernoulli random variables with parameter θ with 0<θ<1. Let T = Σ_iXi and 0 otherwiase. (a) Derive Eo[6(X,, X.)]. (b) Derive Ee16(X, . . . , Xn)IT = t], for t = 0, i, . . . , n.
Consider the random sum S= Xj, where the X, are IID Bernoulli random variables with parameter p and N is a Poisson random variable with parameter 1. N is independent of the X; values. a. Calculate the MGF of S. b. Show S is Poisson with parameter Ap. Here is one interpretation of this result: If the number of people with a certain disease is Poisson with parameter 1 and each person tests positive for the disease with probability p,...
4. (3 points) Let X,.., X be an i.i.d. Bernoulli random variables with parameter p. Is it reasonable to use the exponential distribution to describe the prior distribution of p? Answer 'yes' or 'no ad exain 4. (3 points) Let X,.., X be an i.i.d. Bernoulli random variables with parameter p. Is it reasonable to use the exponential distribution to describe the prior distribution of p? Answer 'yes' or 'no ad exain
Let X1 Xn be a random sample of size n from a Bernoulli population with parameter p. Show that p= X is the UMVUE for p. 5.4.22 Let X1 Xn be a random sample of size n from a Bernoulli population with parameter p. Show that p= X is the UMVUE for p. 5.4.22
If X and Y are Bernoulli random variables with parameters 0.2 and 0.35, which means X~Bo.2 and YBo.35. What is the Bernoulli parameter for the following random variables? If they are not Bernoulli, input -1 .x.y
Recall that a Bernoulli random variable with parameter p is a random variable that takes the value 1 with probability p, and the value 0 with probability 1 - p. Let X be a Bernoulli random variable with parameter 0.7. Compute the expectation values of X, denoted by E[X*1, for the following three values of k: k = 1,4, and 3203. E [X] = E [X4 E [X3203
3. (15 Points) Let Xi Bernoulli(p) and X2Bernoulli(3p) be independent Bernoulli random variables where p E [0, 1/3]. Derive the Maximum Likelihood Estimator (MLE) of p. Denote it by p. 3. (15 Points) Let Xi Bernoulli(p) and X2Bernoulli(3p) be independent Bernoulli random variables where p E [0, 1/3]. Derive the Maximum Likelihood Estimator (MLE) of p. Denote it by p.
Question 3: A random variable X has a Bernoulli distribution with parameter θ є (0,1) if X {0,1} and P(X-1)-θ. Suppose that we have nd random variables y, x, following a Bernoulli(0) distribution and observed values y1,... . Jn a) Show that EIX) θ and Var[X] θ(1-0). b) Let θ = ỹ = (yit . .-+ yn)/n. Show that θ is unbiased for θ and compute its variance. c) Let θ-(yit . . . +yn + 1)/(n + 2) (this...
Xi : i = 1,2,3,4 are independent and identically distributed Bernoulli variables with parameter p= 0.6. Find P(X1=X2), P(X1=X2≠X3), E[2X1+ 3X2−5], and E[(X1+X4)^3].
Let Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter p. Suppose that Y, X1 and X2 are independent. Proof using the de finition of distribution function that the the distribution function of Z =Y Xit(1-Y)X2 is F = pF14(1-p)F2 Don't use generatinq moment functions, characteristic functions) Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter...