If X is a random variable having a geometric distribu-tion, show that P(X = x + n|X > n) = P(X = x)

Q: 1 The discrete random variable X has Var (X) = 5 Find Var (4X – 3)

A: Given Data: Var(X)=5 Equation: Var(4X-3) ......(1) Simplify the equation (1). Var4X-3=42VarX=16VarX

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: Let X, denote a binomial random variable with parameters (n, P.), n z 1 If np, → A as n→ 0, show…

A: Solution

Q: 2. Let X be a random variable. Is it possible that px,x² = 1 for some X? What about PX,x² = -1?

A: Solution

Q: If the probability of occurrence of an event (probability of success) in a single trial of a…

A:

Q: Let (S.lo be a simple random walk starting from 0. Let P(S, 1)= p. if the probability never returns…

A: Given Information: Let Snn≥0 be a simple random walk starting from 0. Let PS1=1=p if the probability…

Q: Let X be a random variable representing a risk with E(X) = 10 and E(X²) = 125. A portfolio contains…

A:

Q: Color blindness appears in 1% of the people in a certain population. How large must a sample be if…

A:

Q: . Let a random variable X - U(5,5+0). Based on a single observation X1, find the unbiased estimator…

A: # random variable x follow uniform (5,5+theta) then to find unbiased estimator of theta^2

Q: A sample of size 200 is taken at random from an infinite population. Given that the population…

A: We have to find given sample proportion...

Q: Suppose that X, and X, are random samples from a binomial distribution of two trials with parameter…

A: The likelihood function of n i.i.d. random variables Xi, i = 1(1)n having the pdf/pmf f(xi) with…

Q: Suppose that the random variable X satisfies P(X=a) = p and P(X=b) = 1-p, where a<b. Verify that…

A:

Q: two students will be picked from a pool of students and W is a random variablethat pertains to the…

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

Q: The characteristic function for a Gaussian random variable X, having a mean value of zero, is ¢, (@)…

A:

Q: Let X1, X2, ... be a sample from a population that is geometrically distributed with p = }. (a) Use…

A: Given: Xi ~ Geometric with p=1/4 Therefore,  E[X] = μ = 1/p = 4   &amp;  Var(X) = σ2 =1/p2 -1/p = 16…

Q: What is the minimum value of  k in Chebyshev's theorem for which the probability that a random…

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Q: Suppose that X1, X2, X3, .., X99, X100 are independent Bernoulli(1/2) random variables. What is…

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: 1. For a nonnegative integer-valued random variable Y, show that EiP(Y >i) =LE(Y*)– E(Y)].

A: The expectation formula is as follows:

Q: rete random variable that possesses a binomial distribution. Using the binomial formula, find P(X=8)…

A: The binominal formula is: where n is the number of trials p is the probability of success on a…

Q: Let X and Y be random variables having the same distribution. 1 If X and Y are independent, show…

A: Given that  Let X and Y be random variables having the same distribution.If X and Y are independent,…

Q: 2. Let X be a binomial random variable with p - 0.1 and n- Calculate the P(X > 8). (Binomial). 10.

A: (As per bartleby guidelines, for multiple questions asked, only the first question will be solved.…

Q: Let x1, x2.X, be a random sample of size (n) taken from N(H1 H2), H2 >0, then alnL(x;2)

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Q: If the random variable X is uniformly distributed between 40 and 50, then P(35≤X≤45) is?

A: The density function is given by: f(x) =1/(50-40)        = 1/10

Q: Let X = (X1, X2)' be a random sample from Po(A), A > 0. Show using the definition %3D chat S(X) =…

A:

Q: suppose that X is a random variable with probability distribution.P(X=k)= 0.02k,where k takes the…

A: Given: P(X=k) = 0.02k k = 8,12,10,20 Here takes the value 8,12,10,20

Q: 4. If X is an integer-valued random variable with characteristic function ø, show that 1 P(X = k) =…

A: Given:-

Q: If x" bin(n1,p) and x2~bin(n2,p) then find the distribution of x1|x1+x2 ; where x1 and x2 are…

A:

Q: For a discrete random variable which takes on nonnegative values (0, 1,2,3, . . .) such as the…

A: whether the given statement is true or false

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

A:

Q: Verify central limit theorem for the independent random variablesX,, where for each k, P{X =± 1} = .

A:

Q: Let x1, x2X. be a random sample of size (n) taken from Poisson( 8), and y = 2x, then F(x1, x2 , X,…

A: Poisson Distribution: A discrete random variable X is said to follow Poisson distribution with…

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

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Q: Let Z be a discrete random variable with ?(Z)0. Does it necessarily follow that E(Z^3)=0? If yes,…

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Q: Let A be a "random point" that coincides with the point a₁, a2, a3 or a4 with equal probabil- ities.…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: let X(n,p) denotes binomial random variable with parameters n and p. Show that X(n+1,p) >st (…

A: Given Information: X(n, p) denotes binomial random variable with parameters n and p where n is the…

Q: If x,,X,. X, be Bernoulli random variables, with parameter 7, then the sufficient statistic for 7…

A:

Q: (a) A stick of length 1 meter is broken into two pieces at a randomly chosen point on the stick.…

A: (a) When we break the stick into two pieces at a point x, we will be left with one piece of length x…

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

A:

Q: If is a random variable that has a uniform distribution on the interval [0, 10], then p(x+ 27) PX+…

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

Q: Assume that X is a uniform random variable on the intery (-22, 14]. (a) Find the probability that X…

A: 11. From the given information, X follows uniform distribution with [-22, 14]. Consider,…

Q: In which three balls are selected simultaneously and randomly from a box. But assume that the box…

A: The possible different number of values for the random variable X are calculated below: Let us…

Q: If X is uniform random variable on interval (2,7) then the expexted value of X equal 9/2 (1/2 (5/2

A: Thanks for the question :)And your upvote will be really appreciable ;)

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 X1, X2, ..., Xn be independent and identically distributed random variables, X ∼ Exp(λ). Show…

A: Given  X1, X2, ..., Xn be independent and identically distributed random variables X ∼ Exp(λ) The…

Q: Letx X2,bp å dzntically distributed random variables with finite second moment Show that nP [Ix) 7…

A: The answer is given using the concept of normal distribution.

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.