6. Suppose X is a continuous random variable with the pdf ?(?) is given by ? ? =1/4+3/2?, 0 ≤ ? ≤ 1; 0, otherwise. a. Verify ?(?) is a valid pdf. b. Find the cumulative distribution function (cdf) of X. c. Find P(0≤X≤0.5). d. Find E(X). e. Find V(X).
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6. Suppose X is a continuous random variable with the
? ? =1/4+3/2?, 0 ≤ ? ≤ 1; 0, otherwise.
a. Verify ?(?) is a valid pdf.
b. Find the cumulative distribution
c. Find P(0≤X≤0.5).
d. Find E(X).
e. Find V(X).
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- In the 2012 presidential election, most Americans were inundated with poll results, all of which reported a margin of error. Discuss what a margin of error means for poll results. What does it tell us and why is it necessary to include this information in poll results?Q1. Suppose that X and Y are jointly continuous random variable ??? 0 < ? < 1 ??? 1 < ? < 2 ?(?, ?) = { 0 y - x ??ℎ?????? (?) ??????? ??? ???? ??(?) ??? ??(?)) (b) ??????? ??? ???? ??(?) ??? ??(?) (c) ??????? ?(?), ???(?), ?(?) ??? ???(?) The picture below also shows the question just incaseA box has 3white(W) balls,2 black (B) balls and 4 red(R) balls. Two balls were drawn successively from this box (i) with replacement/ (ii) without replacement. Let X=the number of white balls drawn and let Y=the number of black balls drawn.
- Q1. let Y₁ < Y₂ < Y3 < Y4 < Y5 are the order statistics of the random sample of size 5 from the distribution : f(x) = 3x², 025. Let X have a three-dimensional normal distribution with mean vector and covariance matrix and A- 3-1 respectively. Set Y= X1 +X + X, and Y= X1+X. Determine the conditional distribution of Y given that Y 0.2. The random variable X is the amount of fructose in apples (in ounces) grown at a local orchard and is represented by the following cdf: 2(x +), 1*2. Let log Y the median of Y). ~ N (u, o2). Find the distribution of Y and show that P(Y < eH) = 0.5 (i.e., el is5.22 a. Form the probability distribution table for P(x) = , for x = 1,, 2, 3. %3D b. Find the extensions xP(x) and x²P(x) for each x. Find E[xP(x)] and E[x*P(x)]. d. Find the mean for P(x) = , for x = 1, 2, 3. 2 e. Find the variance for P(x) =, for x = 1, 2, 3. 6' f. Find the standard deviation for P(x) = *, for o 62 aluvilidsdon х%3D 1, 2, 3.1Example 23. A distribution x1, X2,..., Xp., Xp with frequencies, fp f2,..., f..., fn is transformed into the distribution y1, y2,.….., Y,.., yn with the same corresponding frequencies by the relation y, = ax, + b, where a and b are constants. Show that the mean, median and mode of the new distribution are given in terms of the first distribution by the same transformation.Prove that the events Es, E2... En are independent iff their corresponding indicator variates I,, I₂.. In are independent.5. Assume that X is a discrete random variable with cumulative distribution function (cdf) F(x) given below. F(X) 0-8 0.b t0.2 -2 2 3 ->The random variables A and B have variances 0.2 and 0.5 respectively. Let T= 5A+2B. The variance of T is 6 a. True b. False <SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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