Let Y be a random variable with p(y) given in the accompanying table. Find E(Y), E(1/Y), E(Y2-1), and V(Y).
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Let Y be a random variable with p(y) given in the accompanying table. Find E(Y), E(1/Y),...
Let X be a discrete random variable with 1 P(X = 1) = P(X = 2) = P(X = 3) = P(X= 4) = Then given X = x, we roll a fair 4-sided die 3 times. (The 4-sided die is equally likely to come up a 1, 2, 3, or 4). Let y be the number of times we roll a 1. (a) Find E[Y|X]. Hint: Remember E[Y | X] is a random variable, so X will be part...
(2) Let Y be a binomial random variable with parameters n and p. Remember that E(Y) V(Y)p1 -p) We know that Y/n is an unbiased estimator of p. Now we want to estimate the variance of Y with n(2(1 (a) Find the expected value of this estimator (b) Find an unbiased estimator that is a simple modification of the proposed estimator
Given the random variable Y in Problem 3.4.1, let U-g(Y) Y2 (a) Find Pu(u) (b) Find Fu(u) (c) Find E[U]
9. Let Y be a random variable who probability density function is given by P(Y- y) = 옮 when y is an intger between 1 and n inclusive. What should n be for this to be valid probability density function? Compute E(Y), V(Y), E(17Y - T) and 10, 10% of bottles produced at a factory have cracks. If two bottles are selected, find the mean and variance of the number of cracked bottles selected.
Name: Question 4. Let Y be a discrete random variable with ply) given in the table below. p(y0.2 0.30.5 a) Find the cumulative distribution function (CDF)Fy) Be sue to specify the value of Fly) for all y,y b] Sketch the distribution function given in part [a]
Let X be a discrete random variable with P(X = 1) = 1 4 1 P(X = 2) = 8 1 P(X = 3) = 2 P(X = 4) = 8 Then given X = x, we roll a fair 4-sided die x times. (The 4- sided die is equally likely to come up a 1, 2, 3, or 4). Let y be the number of times we roll a 1. (a) Find E[Y| X]. Hint: Remember E|Y|X] is a...
4. (9 pts) Suppose the random variable Y has a geometric distribution with parameter p. Let ?? = √?? 3 3 . Find the probability distribution of V 3 4. (9 pts) Suppose the random variable Y has a geometric distribution with parameter p. Let V 3 Find the probability distribution of.
Let a random variable X be uniformly distributed between −1 and 2. Let another random variable Y be normally distributed with mean −8 and standard deviation 3. Also, let V = 22+X and W = 13+X −2Y . (a) Is X discrete or continuous? Draw and explain. (b) Is Y discrete or continuous? Draw and explain. (c) Find the following probabilities. (i) The probability that X is less than 2. (ii) P(X > 0) (iii) P(Y > −11) (iv) P...
Let the random variable Y have the following probability distribution y 2 4 6 P(Y=y) 4/k 1/k 5/k find the value of k. find the moment-generating function of Y find Var(Y) using the moment generating function let W= 2Y-Y^2 +e^2*Y+7. find E(W)
Let random variable Y follows Bi(200, .3), Find P(Y 63), P(59 Y 64).