2. If the distribution function of a random variable is given by S(x) = 1–- for x>2 for xs2 Find the Probabilities that on a value random variable will take one value a) less than 3 b) between 4 and 5

Q: Let X be a random variable that takes on values between 0 and c. That is, P(0 < X< c) = 1. Show that…

A: Solution-: Let, X -be a continuously random variable takes values between 0 and c i.e. P( 0≤X≤c)=1…

Q: and X, be independent normally distributed random variables. X,has a normal distribution with mean 1…

A: Introduction - Z-score  z=x-μσwhere , μ=population mean x=score σ=standard deviation +

Q: (2) Suppose that for all n 2 1, the nth momnent of a random variable X is (n+3)3"-1 Find the…

A: Solution

Q: Let X be a random variable having the binomial distribution with size n and probability p E (0,1).…

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Q: Two random variables X and Y are known to be uncorrelated. When considered separately, X is known to…

A: If two random variable X and Y are uncorrelated then Cov(X,Y)= 0 I.e  X and Y are independent. If X…

Q: 4. Suppose that X and Y are random variables having the joint probability distribution Y 2 1 - 3 5…

A: Given,   X=2 X=4 Total Y=1 0.15 0.10 0.25 Y=3 0.25 0.25 0.5 Y=5 0.15 0.10 0.25 Total 0.55…

Q: If X1 and X2 are independent random variables hav-ing binomial distributions with the respective…

A:

Q: Suppose for a random variable X that E(X) = 5 and Var(X) = 3. What is E((X + 3)2)? %3D

A:

Q: X is a continuous random variable taking values between 0 and 2. If F(1.5) = 0.70 and P(X<1) = 0.20,…

A:

Q: 2. Let X1 and X, be independent random variables with mean u and variance o?. Suppose that we have…

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Q: (2) Z is the present value random variable for a pure endowment of 1000 payable at the end of 20…

A: Pure endowment contracts: A pure endowment contract provides the sum assured at the end of the fixed…

Q: The random variable x is known to be uniformly distributed between 0.5 and 2.5. Compute P(x=1.25)

A: It is given that X follows Uniform(a = 0.5, b = 2.5)

Q: Let X and Y be independent normal random variables such that the mean and variance of X are 2 and 4,…

A: Given :  X and Y be independent normal random variables mean of X is 2  variance of X is 4   mean of…

Q: Suppose again that Y is a normally distributed random variable with mu = 10 and sigma = 2. The…

A: Given Data Population Mean,μ = 10.0 Population Standard Deviation,σ = 2.0

Q: Suppose you have a formula: Z = 20 + (1/2)X · Y2 Where X and Y are both random variables. Assume X…

A:

Q: 1. Show that if X' , Y' are the deviations of the random variables X and Y from their respective…

A: Given that, Xi' and Yi'are the deviations of random variables X and Y form their means. Xi' = Xi-X¯…

Q: If X1 and X2 are independent random variables hav-ing the geometric distribution with the parameter…

A:

Q: if Y1 and Y2 are independent Poisson random variable with parameters λ1 and λ2 re- spectively. Then…

A:

Q: A continuous random variable has a p.d.f. ſkx³(1 – x)²0 < x < 1 | f(x) = Ootherwise

A: Given,f(x)={kx3(1-x)2  ;0&lt;x&lt;10                   ;otherwise

Q: 2. A soft-drink machine at a steak house is regulated so that the amount of drink dispensed is…

A: from the given information  sample size n=9 population mean μ=200 population standard deviation σ=15

Q: A continuous random variable X has the distribution function F(x) = 0 if x 3 The value of k is

A: Given:  X has distribution function as : F(X) = 0 if X&lt;1 = k(x-1)^4 if 1&lt;X&lt;3 = 1 if X &gt;3…

Q: b) A random sample of size n, = 25 is selected from a normal population with a mean of 95 and a…

A: b) Given that,

Q: If the discrete random variable X has the pmf for 2-1,0,1,3, a = find E(X), and var(X).

A: Random variables are of 2 types, discrete and continuous. A discrete random variable can only take…

Q: Let X be Poisson random variable with the mean λ. Find the value of λ that satisfies P(X = 0|X ≤ 2)…

A: Let X be a random variable which follows Poisson distribution with a population mean λ. X~P(λ) The…

Q: 7. Suppose that X has a discrete uniform distribution on the integers 0 through 5. Determine the…

A: X has a discrete uniform distribution, P(X = x) = 1/N : x = 0,1,2,3,4,5 N = 5

Q: If the random variable X has a Poisson distribution where the lambda equals 7, Then the different…

A:

Q: Suppose that random variable X is uniformly distributed over the interval (0,1). Assume that the…

A: X follows U(0,1) Y|X follows B(n, x)   E(X) = ½ E(Y|X) =nx

Q: If the random variable X is uniformly distributed over I V3 сотрute V3 30 and compare it with the…

A:

Q: If the random Variable x has a uniform distribution the interval [0,5] on Find P(2<XS4).

A:

Q: 2.) For a continuous random variable X,where c is any one isolated number what is: P(X = c) Hint:…

A:

Q: Suppose that X is a random variable with distribution function given by I< 1, 1<r< 2, 2 <x < 3, 3<r.…

A:

Q: A random sample of size 49 is taken from a binomial distribution with n = 60 and p = 0.4. Another…

A:

Q: Suppose two discrete random variables X and Y follows a Binomial distribution. If the random…

A: A random variable X is said to follow the binomial distribution if its takes only non-negative…

Q: If X is a discrete random variable with the distribution function p(x) = 3-*; x = 1,2,3 ... Prove…

A: Given that the distribution function of the discrete random variable X as px=3-x  ; x=1, 2, 3 ...…

Q: If the time taken to repair a personal computer is a random variable X whose p.d. f is given by · ,0…

A:

Q: For a large number of random variables with identical expectation of 10, and also satisfy all the…

A: By the Law of Large Numbers, here the simple average of the random variables converges to 10 as the…

Q: The probabilities of all the values of a random variable X must: OA. average to a small and negative…

A: Random Variable: In probability theory, a random variable is a variable whose values depend on…

Q: If the joint probability distribution of X and Y isgiven byf(x, y) = 130 (x + y) for x = 0, 1, 2, 3;…

A: Given, the joint probability density function:

Q: Let X1 and X2 be two independent random variables having Gaussian (normal) distribution with means…

A: According to the question: X1 ~ N( 30, 9) and X2 ~N(20, 16) That means X1 - X2 ~ N(30-20 ,…

Q: 2. Prove that if X is a discrete random variable, a and b are constants, and Y = aX + b, then My (t)…

A:

Q: If the discrete random variable X takes on the values 1 , 2 , 3 and if P ( X = 1 ) = P ( X = 3 ) =…

A:

Q: Suppose that discrete random variable X~uni[1,2,3] A random sample of n=36 is selected from this…

A: The question is about sampling dist. Given :  X ~ uni [ 1, 2, 3 ] Sample size ( n ) = 36   To find :…

Q: IfX is a random variable that has a uniform distribution on the interval [o, 10], then pfx+ 10 27 is…

A: Let X be a random variable which has a uniform distribution on the interval [0,10], then the pdf of…

Q: Suppose x is a normally distributed random variable with mean u =0 and standard deviation o = 1.…

A: We'll use formula here and using table we will find the value here . and after that convert that…

Q: Let X denote a random variable having a distribution. If F(x)=ax³ where 0≤x≤(+3). Find f(x) after…

A:

Q: If X is a continuous random variable with distribution, f(x) =*+ k if 0 < x< 3 = 0 elsewhere…

A: if X is a continuous random variable with distribution,f(x)=x6+kif 0≤x≤30elesewhere

Q: (2) Suppose that for all n > 1, the nth moment of a random variable X is (n+3)!3"-1 Find the…

A: Given that,           For all n≥1, the nth moments of a random variable X is…

Q: Suppose that X is a random variable with distribution function given by 0, x < 0, 告, 0 <x < 1, Fx…

A:

Q: The random variable V has a PMF of PV(v) of c(1/2)n when n = 0, 1, 2, 3 and it is 0 otherwise. Set…

A: The function is PMF if ∑Pi=1 so it follows: c120+c121+c122+c123=1c1+12+14+18=1c158=1c=815 Hence the…

Q: X is an poisson random variable with parameter λ = 4 Calculate P {X ≤ 3}

A: It is given that X is the random variable and the mean given by λ is equal to 4 The probability of X…