Suppose the c.d.f. of random variable X is defined as if x < 0 x2/4 if 0 2

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: (1) Let X be a random variable with p.d.f. -8x 0<x<0 k f(x)=. , find k. O.w

A: Step 1: Given,                            f(x) =1k e-8x0, 0&lt;x&lt;∞ We know that ,…

Q: Let X be a nonnegative random variable. Prove that. EX (EX) 4E[X*] 2

A: Given that X be a nonnegative random variable. Result: PX≥c≤E(X2)c2               ≥c2EX2

Q: Suppose X, Y are two discrete random variables with probability function given by: Y X 1/9 1/9 -1 1…

A: There are two type of variable, they are dependent and independent variable. Dependent variable is…

Q: Suppose X, Y are two discrete random variables with probability function given by: Y X-1 1/8 1/8 1/8…

A: Multiplication of marginal probabilities are are compared with joint pmf.

Q: Suppose X is a discrete random variable with finite first and second moments. Show that E (x…

A: It is given that X is a discrete random variable with finite first and second moment.

Q: P(X=0)=P(X=2)

A:

Q: Let X be a random variable with p.d.f. [(k +4)x 1<x<5 f(x) = , find (1) k (2) Var(x) O.W

A: Let X be a random variable with p.d.f. fx=k+4x      1&lt;x&lt;50                  otherwise   1) We…

Q: Suppose that Z is a discrete random variable with Var(Z) = 1/2 and E(Z) = 2. Match up the following…

A: 1] Var(Z)=12 2] E(Z)=2

Q: Suppose the manufacturer of an item wants to test Ho p= 0.8 against H1 p= 05 for a binomial random…

A:

Q: Suppose that X is a binomial random variable with n=300 and p=0.47 Use a normal approximation to…

A:

Q: Suppose that five random variables X1,·.., X5 are i.i.d., and each has a standard normal distribu…

A: It is given that Xi has a standard normal distribution. The sum of two independent normal variables…

Q: Suppose X is a continuous random variable with probability dens function 0.3 0 1 What is the…

A: The variable X is a continuous random variable.

Q: Suppose x is a random variable with deneity function given by: (kx 0sxs1 f(x)=- otherwise Compute…

A:

Q: Suppose that X is a binomial random variable with n=230 and p=0.48. Use a normal approximation to…

A: Given data, n=230 p=0.48 P(X≥100) = ?

Q: Let X be a random variable with p.d.f. 3e-3x 0<x<0 f(x) =- find E(e*) O.W

A: As per our guidelines we are suppose to answer first question .

Q: Suppose a random variable X is claimed to have the cumulative distribution func- tion (CDF) F(r) =…

A: Given cumulative distribution function (CDF)                                               F(x)=xx+1…

Q: For a continuous random variable x, the probability that x assumes a value in an interval is: less…

A:

Q: Let X be a random variable with p.d.f. 1. x = 1,2,3,4 f(x) = find Var(x) o.w

A: The formula for computing var(x) is, var(X)=E(X2)-(E(X))2 HEre, E(X)=∑x*f(x)and  E(X2)=∑x2*f(x)

Q: Let X be a discrete random variable with PMF: (0.33 for k = 0 0.27 for k = 1 | 0.15 for k = 2 Px(k)…

A: From the given information, X be a discrete random variable with PMF, PXk=0.33 for k=00.27 for…

Q: Suppose the discrete random variable X has probability function 1. px(1) I = 1,2, 3, I(I +1)"

A: Given  :    pxx  =1xx+1,  x=1,2,3,...

Q: Suppose the p.d.f. of random variable X is defined as x³/20 if1<x< 3 f(x) = otherwise

A:

Q: Suppose N is a Poisson random variable with mean A. Show that E (1+ for any constant a. +a)^

A: Hello! As you have posted 2 different questions, we are answering the first question (4-2). In case…

Q: If we let kσ = c in Chebyshev’s theorem, what doesthis theorem assert about the probability that a…

A:

Q: Suppose the commulative distribution function of the random variable X is given by if x<-2 -(x+2) if…

A:

Q: random variable

A:

Q: (1) Let X be a random variable with p.d.f. -8x 0<x<0 k f(x)=- , find k. O.w

A: Given: The probability density function of the random variable X is given as:…

Q: 7. A discrete random variable X taking non-negative integer values has probability gen- erating…

A:

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

A:

Q: Suppose that X is a random variable for which E(X) = μ and Var(X) = σ2. Show that E[X(X − 1)] = μ(μ…

A:

Q: Let X be a random variable with p.d.f. ((k +4)(x+2) f (x) ={ 0<x<2 , find (1) k (2) E(x) O.W

A: (a) We know, ∫fx dx=1∫02k+4x+2 dx=1∫02kx+2k+4x+8 dx=1kx22+2kx+2x2+8x02=12k+4k+8+16=16k=-23k=-236

Q: Find the distribution of Z X+Y, if X and Y are jointly continuous random variables F given by

A: Given information: The joint probability density function of the random variables X and Y is given.

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

A: Given function is f(x)={x6+k    0≤x≤30          elsewhere

Q: - Prove that the moment generating function of the random variable X having the p.d.f. fx (x) =, -1<…

A:

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: Let X be a random variable with u = 4 and o = .5. (a) Use the Chebychev inequality to estimate Pr(3…

A: Chebyshev’s theorem: When the distribution of the population is not known. That is, when there is no…

Q: (1) Let X be a random variable with p.d.f. -8x 0<x<0 k f(x)=< , find k. O.w

A: Given information: It was stated that X is a random variable. The probability distribution…

Q: 2. Suppose that a random variable X has a discrete distri- bution with the following p.f.: cx for x…

A:

Q: A screening test for a particular infectious disease shows a positive test result in 90% of all…

A:

Q: Let X be a random variable with p.d.f. 2e-2x 0< x<00 f(x) = , find E(x). O.w

A: We know that, E(x)= integration |x X*f(x) dx

Q: Let X be a random variable with p.d.f. k 1<x<00 f(x) = , find k. O.w

A: According the theorem of probability the sum of all the probabilities is equal to one, that is…

Q: With reference to Definition 4, show that μ0 = 1and that μ1 = 0 for any random variable for…

A: The value of μ0 is calculated as follows: μ0= E(X-(E(x)))0      = E(1)      =1

Q: Let X be a continuous random variable. Which of the following quantities are definitely equal to P(X…

A:

Q: Suppose that the probability distribution function for the random variable X is given by: 2X f(X) =…

A: There are two types of variables : Continuous variables and discrete variables. Continuous variables…

Q: (4) Let X be a discrete random variable with domain D. Prove that Var(X) = E(X?) – E(X).

A:

Q: Let X be a random variable with p.d.f. (k 1<x<10 f(x)=- find k. O.W

A: Solution: 11. From the given information, the probability density function of X is

Q: Suppose that X is a discrete random variable with P(X = 0) = 0.3, P(X = 1) = 0.2, P(X =2) = 0.15,…

A: Given X is a discrete random variableP(X = 0) = 0.3P(X = 1) = 0.2P(X = 2) = 0.15P(X = 3) = 0.35 The…

Q: 1. Given that x is a continuous random variable that is uniformly distributed in a range from 8 to…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: 4.Suppose that X is a random variable for which E(X)=µ and Var(X)=o². Show that E(X(X-1)]=µ(µ-1)+o?

A: It is given that E(X) = μ and Var(X) = σ2

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.