Suppose that three random variables x,„X,„X, fom a random sample from the uniform distribution on the interval [0,2], and they are independent. Determine the value of Е(2X, —3х, +х, -4). Var(2X, —3х, +х, —4) and E(2х, -зх, +х, —4)*|
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- Let a and b be any real numbers and let x = (x1,Xz -- -- Xp m-, X) be a data set with a sample mean f and a sample variance s. Show that if y, = (ax, + b), then S3 = a*s;An ordinary (fair) coin is tossed 3 times. Outcomes are thus triple of “heads” (h) and tails (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hht, then R (hht)=1. Suppose that the random variable X is defined in terms of R as follows X=6R-2R^2-1. The values of X are given in the table below. A) Calculate the values of the probability distribution function of X, i.e. the function Px. First, fill in the first row with the values X. Then fill in the appropriate probability in the second row.X~ N(60,9). Suppose that you form random samples of 25 from this distribution. Let X- be the random variable of averages. Let £X be the random variable of sums. To make you easy, drawing the graph, shade the region, label and scale the horizontal axis for X-, and find the probability. X-~N(60,9/ radical 25). Find P(18< X-<58).
- Suppose that the random variables X and Y are independent with Var(X)=8 and Var(Y)=6. Calculate Var(5X−7Y+17)the random variable Y is such that : E(2Y+3)=6 and Var(2-3Y)=11 find E(Y^2)A random variable Y has a uniform distribution over the interval (8,, e,). Derive the variance of Y. Find E(Y)? in terms of (e,, e,). E(Y)? = Find E(Y) in terms of (e,, e,). E(Y) = Find V(Y) in terms of (8,, e,). V(Y) =
- If X1, X2, ...Xn is a random sample from N(0, σ^2), How would you show the following?Let X and Y are 2 independent random variables N (0,1) Questions: how to find E(X), E(Y), E(X^2), E(Y^2)? Thank yousuppose the random variable x denotes students scores on a test worth 150 points. Let X~N(120, 60). Find the probability that a randomly chosen student passes the exam (a score of at least 73%)
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