..BERSAMA DI...4G 3:18 PMDoneQ2 a Sta Mid term.pngQ2 (a) The discrete random variable has the probability distribution as in Table Q2.Table Q2: Probability distribution functionX01345P(X)1h11136918Find(11)Calculate the mean and variance.E(2X + 2)(iv)Var(3x + 1)1 74%A

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Answered: Q2 (a) The discrete random variable has…

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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In a school sports day, each student is required to join at least one event. The following table represents the probability distribution function of the number of events (X) a student takes part in the sports day. 1 3 4. P(X=x) 0.25 0.375 1.5k k 0.05 (a) What is the value of k? (b) Find E(X) and o (X). (c) Suppose the number of events students take part are independent. In a group of 6 students, what is the probability that exactly 4 students join at least 2 events?
The random variable X has the probability distribution table shown below. 8. 10 12 14 P(X = x) 0.2 0.2 a a 0.2 (a) Assuming P(X 10) = P(X = 12), find each of the missing values. a = (b) Calculate P(X > 10) and P(6 10) P(6 < X < 12) :
A random variable X has a following probability function, X 0 1 3 4 5 6 P(X) 0k 2k 2k | 3k k 2k 7k2 + k Find the value of, (i) k (ii) P(X < 6).
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Trying to find variance. his equation is Prob(x)*[x-e(x)]^2. Just need an example to get me started.Original question is: A call center recieves an average of 10 calls per hour. Assuming the number of calls received follows the poisson distribution, determine the probability of each of the discrete outcomes below. Then calculate the variance component for each one using the standard formula for the variance of a discrete random variable. At the end, take the sum of both columns. Table: Poisson Distribution Table Calls Density Variance 0 0.00% 1 0.05% 2 0.23% 3 0.76% 4 1.89% 5 3.78% 6 6.31% 7 9.01% 8 11.26% 9 12.51% 10 12.51% 11 11.37% 12 9.48% 13 7.29% 14 5.21% 15 3.47% 16 2.17% 17 1.28% 18 0.71% 19 0.37% 20 0.19% 21 0.09% 22 0.04% 23 0.02% 24 0.01% 25 0.00% 26 0.00% 27 0.00% 28 0.00% 29 0.00% 30 0.00% Sum 100.00%
Consider a random sample X1,..., X, with n > 3 from the exponential distribution with parameter ) > 0 and density 1 f(x; A) = x > 0. Consider the following two estimators of X: 3 1 ΣΧ, Ã = nX(1). 3 i=1
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Q2 (a) The discrete random variable has the probability distribution as in Table Q2. Table Q2: Probability distribution function X 0 1 3 4 5 P(X) 1 h 1 1 1 - 3 6 9 18 Find (11) Calculate the mean and variance. E (2X + 2) (iv) Var(3x + 1)