5. The n candidates for a store manager have been ranked 1,2,3,..,n. Let X= the rank of a randomly selectedcandidate, so that X has pmfp(x) - 1/n x=1,2,3..,notherwise(this is called the discrete uniform distribution). Compute E(X) and V(X) using the shortcut formula. [Hint: Thesum of the first n positive integers is n(n+ 1)/2, whereas the sum of their squares is n(n+ 1)(2n + 1)/6.]

The mean of the probability distribution can be obtained as follows:

Answered: 5. The n candidates for a store manager…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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3. Draw the cumulative distribution functions of the following distributions: (a) A continuous random variable chosen uniformly from the interval [1,6]. (b) A continuous random variable chosen uniformly from the union [1,2] U [3, 4] U [5, 6]. (c) A discrete random variable chosen uniformly from the set {1, 2, 3, 4, 5, 6}.
4. Suppose X₁, ..., Xn are iid from a distribution with the pdf (e-(2-0) x > 0 f(x; 0) = for some 0 € R. Find the MLE of 0. 34 35 We went PATRULLA 15 2 271 34000 3 envelar 05352 25000- 0 otherwise
Using the joint distribution describing X and Y, the following formula was derived E(XKym) = 2km+3(m+k)+4 (k+1)(k+2)(m+1)(m+2) where k and m are both nonnegative constants. Simplify Var( 2X - 3Y) [ Select ] - Var(X) [Select] [ Select ] Var(Y) [Select] [ Select ] Cov(X,Y)
A.2) The time between successive customers coming to the market is assumed to have Exponential distribution with parameter lambda. a) If X1, X2. ..., Xp are the times, in minutes, between Successive customers selected randomly, estimate the parameter of the distribution. b) The randomly selected 15 times between successive customers are found as 1.8, 1.2, 0.8, 1.4, 1.2, 0.9, 0.6, 1.2, 1.2, 0.8, 1.5, 1.8, 0.9, 1.5 and 0.6 mins. Estimate the mean time between successive customers, and write down the distribution function. c) In order to estimate the distribution parameter with 0.4 error and 4% risk, find the minimum sample size.
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Let X1 and X2 be observations of a random sample of size n = 2 from a Cauchy Distribution.Find P(X1 < −1 and 1 < X2)
X~ N(70, 11). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let EX be the random variable of sums. O Part (a) Sketch the distributions of X and X on the same graph. 55 60 65 70 75 80 85 O 55 60 65 70 75 80 85 O 55 60 65 70 75 80 85 55 60 65 70 75 80 85 O Part (b) Give the distribution of X. (Enter an exact number as an integer, fraction, or decimal.) X -n (O-0) O Part (c) Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.) PX< 70) = O Part (d) Find the 40th percentile. (Round your answer to two decimal places.) O Part (e) Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.) P(66 < X< 72) = | O Part () Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four…
w that the mle of is = mle of ₹ is V = max{0, X}. 6.1.12. Let X₁, X2,..., Xn be a random sample from the Poisson distribution with 0 <0 ≤ 2. Show that the mle of 0 is 0= min{X, 2}. 6.1.13. Let X1, X2,..., Xn be a random sample from a distribution with one of -²/2 two pdfs If A - 1 then flr: A - TC

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