4.6. The distribution of a random variable X, whose rangeisa, 0, a), is given byP{X = -a} = P₁,P{X=a} = P2Given that X has mean 0 and variance 1, work out the val-ues of p1, P2 in terms of a.

The distribution of a random variable X, whose range is {-a, 0, a} is given by: PX=-a=p1 PX=a=p2…

Answered: 4.6. The distribution of a random…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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An urn contains 7 black and 18 white balls. A ball is randomly drawn from the urn. Let X = 1 if a white ball is drawn and let X = -1 if a black ball is drawn. Find the following a) mean of X b) variance of X Please provide your working and round your answers to 2 decimal places
7. Let (z,.,) be a random sample from a normal distribution with mean ja and a variance at. Alo let S.. = , - z)* be the sum of squares of the randou sample. State without proof the sampling distribution of the following; (a) t(z) - ạ + b i-, 1,. n, as e positive eal constants. (- ) (b) t(z) - (E) (x) = (e) ti2) - (g) (r) = (e) t(2) = (d) t(a) Er, - E > ( - P (h) 시)- - -1 (-) (e) t(z)
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the data support the claim that the average ACT composite score of students from this students is randomly selected from a local high school with an X = 23 and s = 5.2. Do ACT composite scores are normally distributed with a u = 21. A sample of 25 students is randomly selected from a local high school with an X= 23 and s =5.L.D high school is different than 21 on the ACT composite score, using x = .05?
3.4 Solve the below problem: Let Y, and Y, have a bivariate normal distribution: 2. 1. 2. Y2-H2 exp 2no,02y1-p2 2(1-p2) {. (ज-र.) + ( ज-र) (ज-पदर) 07 (जब)} Dr= –00 < y, < ∞, -00 < y2 < ∞, Show that the marginal distribution of Y, is normal with mean µz and variance o is given by: 2, 1 f(y2) = 203 ,-00 < Y2 < ∞ 2.

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4.6. The distribution of a random variable X, whose rang isa, 0, a), is given by P{X = -a} = P1, P{X=a} = P2 Given that X has mean 0 and variance 1, work out the val ues of p₁, p2 in terms of a.