Problem 7For each of the following random variables, find P(X5), P(2

Part a: X ~ Geometric(1/5)P(X>5)=0.3277: This indicates the probability that the first success…

Answered: Problem 7 For each of the following…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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If we let X1, X2,...X10 be a random sample from the distribution N( μ, σ), then what is the value k so that: P( (X-μ)/(σ/√10) < k ) = .05 P( (X-μ)/(S/√10) < k ) = .05 P( k < (X-μ)/(S/√10) ) = .05
Suppose the distribution of some random variable X is modeled as Negative binomial with parameters, p and r, where p is the probability of success and r is the total number of success over the trials. Find the method of moment (MM) estimators for (p,r), in closed algebraic form expressions based on a random sample of size n, X1, X2,...,Xn.
Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
4.1 Let X have a geometric distribution, that is p(x) = q*-'p x = 1,2,3, .. Where X has the memoryless property given by: P(X > k + b|X > k) = P(X > b). Given that you have already tossed a balanced coin 5 times and obtained Zero heads, what is the probability that you must toss it at least 3 more Times to obtain the first head?
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.
34. Suppose that X is a random variable with MGF M(t) = (1/8)e + (1/4)e + (5/8)e. (a) What is the distribution of X? (b) What is P[X= 2]?
If a discrete random variable X has the following probability distribution: X -2, - 1, 0, 1, 2 P(X) 0.2, 0.3, 0.15, 0.2, 0.15 Use this to find the following: (a) The mean of X and E[X^2]. (b) The probability distribution for Y = 2X^2 + 2 (i.e, all values of Y and P(Y )). (c) Using part (b) (i.e, the probability distribution forY ), find E[Y ]. (d) Using part (a), verify your answer in part (c) for E[Y ]. **Note: Please do not just copy from Chegg!
16) number of medical tests that a patient will have on entering a hospital is a random variable X which can take on the values 0, 1, 2, 3, and 4. If P(X 2)=0.43, find P(X = 3).
A taxi company is trying to decide whether to purchase brand A or brand B tires for its fleet of taxis. To esti- mate the difference in the two brands, an experiment is conducted using 8 of each brand, assigned at random to the left and right rear wheels of 8 taxis. The tires are run until they wear out and the distances, in kilome- ters, are recorded in the accompanying data set. Find a 99% confidence interval for u – µ2. Assume that the differences of the distances are approximately normally distributed. Figure 1: A picture of a gull. Taxi Brand A Brand B 48,200 34,900 34,000 45,700 44,200 39,200 40,200 41,600 49,500 35,400 35,500 44,400 43,500 42,700 41,400 42,600 (a) (-2000.44, 900) (b) (-2682.22, 932.225) (c) (1278, 1900) (d) (-1289.12, 211.79) 1234 567CÓ
X is a normally normally distributed variable with mean u =10 and standard deviation a =4. Find A) P(x 1) C) P(10
Let X be a random variable that can take values x = 2,4,6,8 and has probabilities given by the function P(X = x) = 3x/60 Find (1) P(X = 4) (2) P (X ≤ 6) (3) P(X < 6) (4) P (X ≥ 3)
1. Given that X~N(39,32)A Random variable X is normally distributed and has a mean of 9 C Random variable X is not normally distributed and the mean is 39 B Random variable X is normally distributed and has a mean of 3 D Random variable X is normally distributed and the mean is 39

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Problem 7 For each of the following random variables, find P(X5), P(2