Exercise 2 Suppose that N is a Poisson random variable with parameter µ. Suppose that givenN = n, random variables X₁, X2...., Xn are independent with uniform (0, 1) distribution. So thereare a random number of X's.a) Given N = n, the probability that all the X's are less than t is t", where 0

Solution: From the given information, N is a Poisson random variable with parameter µ. The random…

Answered: Exercise 2 Suppose that N is a Poisson…

A First Course in Probability (10th Edition)

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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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pls only answer b-c i am having a hard time understanding those and would like to learn esspecially with plotting residuals. pls use ms excel and thank u
2. a) Let X and Y be independent identically distributed binomial random variables, X~ Bin(3, 0.4) and Y ~ Bin(3, 0.4). i) Compute the probability P(X = 0). ii) Compute the probability that the product XY equals 0, that is, compute P(XY = 0). b) The actual amount of jam (in g) that a filling machine puts into "150 g" jars may be looked upon as a random variable having a normal distribu- tion with σ = 6 and mean μ = 155. What proportion of jars, in the long-run, contain less than 150 g? N(0, 1), Give your answer in terms of the function, where for Z (z) = P(Z), and a give a sketch of the normal curve with a shaded area that corresponds to the required probability.
5. Let X and Y be independent random variables with each following N(0,1). Consider the random variable W defined by { if XY > 0, if XY 0 and W < 0. Show work.
Q1) 14% of the adults in a certain population are infected by a Corona Virus. Five adults are selected randomly from this population for diagnoses. Find the probability that at least two of them will be infected by .this Virus 1 .Q2) Suppose that f(X)=X,12). a) Find .b) Find the mean Q3) A study shows that the systolic blood pressures for adults in a certain population are approximately normally distributed with mean of 115 and .standard deviation of 10 a) Find the probability that a randomly selected person will have a blood -pressure between 109 and 124 Sel).b) Find the reading that is exceeded by only 5% of the population التي يتجاوزها 5% من المجتمع(
A docs.google.com/forms/d/e (1) Let X be a random variable with p.d.f. fx) =- , then O.w (b) k- (0) k = (a) k=1 (d) k-5 (e) None of these a is the correct answer b is the correct answer c is the correct answer d is the correct answer e is the correct answer (2) Let X be a random variable with a function x= 0,1, 2,3 4 x! (3-x)! f(x) = , then p(x<1) is 0.w (b) (d) (e) None of these 27 (a) 27 (c) 27 a is the correct answer b is the correct answer c is the correct answer d is the correct answer e is the correct answer
Suppose that X;; i = 1,2, 3, .. n are independent random variables with a common uniform distribution over (0, 1) and Yg is distributed over (0, Yg -1) with Y, =1,k = 1,2, ..., n. Let Z = k = 1,2,3, .n R.D.R EGALA STAT 203 March 4, 2021 Show by mathematical induction induction or any other method that Zg has probability density function (-In z)*-1 fR(z) = k = 1,2,3, . n (k – 1)! Hence deduce that Zg and Y, have the same distribution (k = 1,2,3, ..n)
Suppose that discrete random variable X~uni[1,2,3] A random sample of n=36 is selected from this population. Find the probability that the sample mean is greater than 2.1 but less than 2.5, assuming that the sample mean would be measured to the nearest tenth.
Let X(1), X(2), ..., X(n) be the order statistics of a set of n independent uniform (0, 1) random variables.Find the conditional distribution of X(n) given that X(1) = s(1), X(2) = s(2), ..., X(n-1)=s(n-1).
Let Y1, Y2, Y3 denote independent exponential random variables with respective rates A; for i e {1,2, 3}. Answer the following questions; (a) Compute E[Y1 +Y2 +Y3]Y1 > 1, Y2 > 2, Y3 > 3]. Your answer should be an expression using A;'s. (b) Compute the probability that Yı is the smallest among three random variables. Hint: P(X < Y) = S" Px,y (x, y)dædy where Px,Y (x, y) is the joint density function.
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