Part A) Let Y., Ye, Y3.. Ym each with probability mass function... be independent random varia bles ()(1-Py ,と=9:○

Q: what is the value of the constant c for plx) to qualify probability mass function? plx) = d if x =…

A:

Q: c) For a gearbox of an excavator, a pair of gear operates at low speed. If the lifetime of the pair…

A: The lifetime of the pair of identical gear follows Weibull distribution with the parameter α=0.0002…

Q: If X is a continuous random variable with the uniform distribution on [0,1], then what is P[X = .5]?…

A: We have given that X is a continuous random variable with the uniform distribution on [0,1].

Q: SV) ="(3y² Sh(3y² + 2) ; -2<ys2 0; otherwise

A:

Q: Let XX and YY be independent random variables. Suppose ~Pois(1), Y~Pois(2) and W = X + Y. a)…

A: If X and Y are independent then P(X=x,Y=y)= P(X=x)*P(Y=y)

Q: Let X1,.X, be a random sample from a uniform (0,0) distribution and let Y = max(X1,..., the coverage…

A: We have a sample X1, X2,....,Xn from uniform distribution.  We know that, Y = max(X1, X2,....,Xn) =…

Q: The cumulative distribution function for a random variable T is given as (0, t7, Find (а)Р(Т %3D 5).…

A: a PT=5=34-12=14=0.25 b PT&gt;3=14+14=12= 0.5

Q: If X is a random variable having a uniform distribution U (a,b) such that P(20<X<40)=D0.2 and mean…

A:

Q: If the variance of a poisson variate is 3. Find the probability that X = 0 i) i) ii) 0<x<3 18x<4

A:

Q: A)lf a grown man is picked at random and his QT interval measured, what is the probability of the…

A: Given X~ N(400, 20^2)  We want to find  (1) P(X&gt;420)= ? (2) P(400&lt;X&lt;420)= ?  (3) P(X&lt;a)=…

Q: The members of University of cape Town Volleyball group are selling branded UCT caps from room to…

A: The sample size is .The probability that the group will sell at least one cap in any room is .

Q: For a uniform random variable U∼U(0,14)U∼U(0,14), find the probability P(U>11)P(U>11): P(U>11)

A: From the provided information, U~U(0, 14) a = 0 and b = 14

Q: A boy is to sell lemonade to make some money to afford some holiday shopping. The capacity of the…

A: It is mentioned that the capacity of lemonade is equal to 1. The two random variables X and Y are…

Q: let X be a random variable and X is normally distributed

A: Given information:  μ=35 and σ=4

Q: Let X and Y be two independent normal rvs with means u = 10 and u = 4 and standard deviations o, = 2…

A:

Q: Afx is a normal distribution variable, then, the moment generating function is eloT2)

A:

Q: Let X1, X2,..., Xn ~ N(μ, 0²) independent random variables. Find the distribution X+X2+…+Xn X= = n…

A: Given Xi~N(μ, σ2) be the iid and i=1,2,...,n  Result: X and Y are independent then E(XY)=E(X)E(Y)…

Q: For a uniform random variable U∼U(2,11)U∼U(2,11), find the probability P(U<9)P(U<9): P(U<9)=P(U<9)=…

A: GivenA random variable x~Uniform(2,11)f(x)=1b-a      ; a&lt;x&lt;bf(x)=111-2f(x)=19  ;…

Q: Q6) Let X be a normal random variable with mean equal to 40 and standard deviation 12. Find the…

A: Solution: Note: Hello! As you have posted more than 3 sub parts, we are answering the first 3…

Q: Consider a random variable X with possible outcome:0,1,2...... Suppose that P(X=j) = (1-a)a^j,…

A: P(X=j) =(1-a)aj , j=0,1,2,... 1. For model to be meaningful 0 &lt; P(X=j) &lt; 1 So,…

Q: iv) P(z < –1.96) v) P(-1.96 < z) vi) P(-2.38 <z < -1.03)

A: b Obtain the probability of z less than –1.96. The probability of z less than –1.96 is obtained…

Q: The random variable Y has normal distribution with a mean of 30 and a variance of 16, i.e. Y~ N(30,…

A: Given,

Q: Q': The probability of a design (A) to be successful is (18/30) and to be successful from design (B)…

A: GIven, For design A: Probability of Successful = 1830 = 0.6 Probability of failure = 1 - 0.6 = 0.4…

Q: Let X be a binomial random variable with mean u = 3.6 and %3D variance o? 2.52, find %3D

A: Givenmean(μ)=3.6variance(σ2)=2.52

Q: B4 Let X,,X,..,X„ be a random sample from the exponential distribution with mean e, and let…

A:

Q: Let X and Y have a bivaraite gamma distribution of Kibble with parameters a = 1 and 0<0< 1. What is…

A:

Q: Let X be a Poisson random variable with parameter λ. Show that the probability that X is even is…

A: Given that, X be a Poisson random variable with parameterλ. We need to show that the probability…

Q: 6). If X is a binomial random variable with n=6 and p=0.4, the probability P(X21) is A) 0.2333 B)…

A: Q-6)binomial distributionn = 6p = 0.4P(x≥1) = ? Q-7)binomial distributionn = 9p = 0.4standard…

Q: 1). Let Z be standard normal random variable, find b such that P(Z > b)= 0.1251 01115 15 C) 2.24…

A: standard normal distribution Z~N(0,1) P(z&gt;b) = 0.1251 b = ?

Q: The length of eels (in cm) in a river may be assumed to be normally distributed with a mean of u =…

A:

Q: Consider the probability distribution for the number of red pens when 4 pens are selected at random…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Let T be the random variable that models the lifespan of a cellphone battery (in months). It is…

A: Given that, T be the random variable that denotes the lifespan of a cellphone battery. The lifespan…

Q: The independent RVs X and Y have distributions N(45, 2) and N(44, 1.5) respec. tively. What is the…

A:

Q: Suppose a random variable X a is a normally distributed random variable X ∼ N(μ,σ2) with μ = 1.50…

A: INTRODUCTION:  NORMAL DISTRIBUTION: Let x be a continuous random variable is said to follow normal…

Q: Y)~ N₂(4, 5, 9, 4,-0.5). What is the conditional distribution of Y given X = 1?

A: Given that  (X,Y)~ N2(4,5,9,4,-0.5) Where μ1=4 , μ2=5 ,?12=9 , ?22=4 And ρ= -0.5 So follow normal…

Q: OLAG X is a normally distributed random variable with u = 25 and o = a) What is the 85th percentile…

A:

Q: The distances travelled to work by the employees at a large company, D km, are normally distributed…

A: Solution

Q: b) Let Z₁: = X-X~N(0,1), and W₁=Y-Y~N(0,1), for i = 1,2,3,...,10, then: oy i) State, with…

A: Given Zi~N(0,1) and Wi~N(0,1)  Result: t~F(a,b) Then  Mean=E(t)=b/(b-2)…

Q: Let Xi and X2 be independent random variables each having the standard normal distribution. Consider…

A: Given that x1 and x2 random  variable

Q: Suggest any value, Zo, of the standard normal probability distribution (correct to two decimal…

A: Let the value of z0 be 1.23.   a) Then , from the left tailed z-tables,…

Q: Suppose we have independent random variables Yi,...,Yn with ..... Y; = 0x; + ei, i = 1,...,n, iid…

A: It is given that Y1, Y2, ......... , Yn are independently random variables with x (constant),θ is…

Q: a) Show that the pmf is well defined b) Determine Mx, also called the expected value of X. Interpret…

A:

Q: Let X and Y be two independent random variables distributed uniformly on the interval [0, 1]. What…

A:

Q: Let X₁, X2, X3, ..., Xn be a random sample of size n from population X. Suppose that X~N (8,1) Σ and…

A: Given  X~N(θ,1) ; i=1,2,...,n