Let X1, X2, . . . are independent indicator variables with different probabilities of success. That is, P(Xi = 1) = pi. Define Yn = X1 + X2 + . . . + Xn. Find E(Yn), V ar(Yn) and coefficient of variation of Yn

Q: Let X1,...,X, be a random sample from (1+ 0x) f(x) = 2 ,-1< x < 1, -1 < 0 < 1. Find the consistent…

A: The random sample consists of X1,X2,...,Xn. Need to obtain: The consistent estimator of θ. The…

Q: If X and Y are two independent random variables such that E[X]=2, variance of X = o}, E[Y]= 1, and…

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Q: 2. Define the process, t I VY(u)dW(u) + | Vudu Y(t) = What is the variance of Y (t)?

A: Solution Given   Y(t)=∫0tY(u)dW (u)+∫0tuduwe need to find the Y(t)?

Q: If the variance of a Poisson variate is 3. Find the probability that, ne (1) x= 0 (ii) 1sx<4 ca eor…

A: Given that, The variance of a Poisson variate is 3

Q: 1. determine the likelihood function L(x: 0) = f(x₁,x2,...,xn|0) and the maximum likelihood…

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Q: If X1, X2, ... , Xn constitute a random sample of size nfrom a geometric population, show that Y =…

A: Factorization Criteriom ( Due to Fisher)Let x⏟= (x1, x2,.....,xn) be a R.S from PME f(xiθ).…

Q: If X and Y are two random variables, then the covariance is Cxy = Ryy – XY

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Q: If X is a Poisson variable such that P(X = 2) = 9P(X = 4) +90 P(X = 6), %3D %3D %3D find the mean…

A: Both the above given questions are same I am giving Answer one of them.

Q: Prove that if 'X' and ʼY' are 'random variables taking real values then [E(XY)}]SE[X°] • E[Y²].

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Q: If X and Y are two random variables, then the covariance of x+a,Y +b,where a and b are constant is…

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Q: Let the random variables X1 and X2 denote the length and width, respectively, of a manufactured…

A: Given: Mean of X1 =EX1=2 Standard deviation of X1 =SdX1=0.2 Mean of X2 =EX2=4 Standard deviation of…

Q: Let Y1 =;(X2 - X2), Y2 = X2 where X1 and X2 are stochastically independent random variable each…

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Q: X and Y are two random variables with variances o? and o,? respectively and r is the coefficient of…

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Q: Suppose that X1, X2, ... , Xn are an iid sample from the distribution given below, f(X)e =…

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Q: Consider a random sample Y1,Y2, ., Y, from a population with mean µ and variance ơ². Calculate the…

A: Given that Y1, Y2,....,Yn from a population with mean μ and variance σ2. M^=1197Y4+3Y5+7Y7+2Y19…

Q: Let XB and XA denote, respectively, the weight of a person before and after a certain weight loss…

A: (i) True Explanation :  A t-test for two paired samples is a hypothesis test that attempts to make a…

Q: Let the random variable X and Y have the joint p.d.f. [12xy(1-x) f(x,y)= 0 Find E[X] and Variance o…

A: Given f(x,y) = 12xy(1-x)    0&lt;x&lt;1     0&lt;y&lt;1

Q: Let B, denote the present value random variable for a continuously increasing contingent payment…

A: Given :f(t)=0.02          for 0≤t≤50We are find the variance B¯x.

Q: I. If X1, X2, ...,Xn constitute a random sample from a population with the mean µ, what condition…

A: An estimator c is said to be unbiased estimator of µ is E(c) = µ.

Q: 20. The lines of regression of y on x and x on y are, respectively, y= x+ 5 and 16x -9y 94. Find the…

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Q: Let X and Y be continuous random variables with joint p. d. f. f(x, y) = {2 if 0 <y<1-x;0 <x<1…

A: The joint probability density function is fx, y=2 if 0&lt;y&lt;1-x ; 0&lt;x&lt;10, elsewhere

Q: 2. Let X be a random variable with pdf fx(x), and Y = X². %3D (a) Find fx(x|X > 0) (b) Find fy(y|X >…

A: We have to answer questions based on conditional pdf of distribution

Q: 2. (a) If Z = aX + bY and r is the correlation coefficient between X and Y, show that of a*ož + b'ož…

A: Given: Z=aX+bY  r=correlation coefficient between X and Y

Q: If X and Y are any random variables with COV(X, Y) = 0.25, o = 0.36, and o = 0.49, then the…

A: From the given information, Covx,y=0.25         σ2x=0.36         σ2y=0.49 Thus,

Q: Ql: a) Suppose that Y,.,Y, represent a random sample such that E(Y,)= u, E(Y} )= µ; , E(Y*)= 4. Show…

A: a)

Q: For the random variable transformation Y=X*X, the value of the expectation of Y is equal to E[Y]

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Q: If x and y are independent random variable with E(xy)= 20 then the correlation coefficient is

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Q: 3.7 Consider the performance function Y = 3X1 – 2.X½X2 where X1 and X, are both normally distributed…

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Q: Suppose the random variable X has pdf K exp 12V/28 XP ( - ("=2)²). fo 2√/2K 0. £x(u) = 0≤u≤ 4,…

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Q: Given any two random variables X and Y, by the linearity of expectation we have E[X – Y] = E[X] –…

A: Given that the two random variables X and Y are independent. By the linearity property: EX-Y=EX-EY…

Q: Find the covariance and the correlation coefficient between X and Y, if X and Y are jointly discrete…

A: For the given data Find the covariance and correlation between x and y

Q: 14. If t is the most efficient estimator and ť is a less efficient estimator with efficiency e and p…

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Q: 4. Suppose the joint PDF of two random variables X and Y are given below. |3(ry? + x²y), if 0 < x <…

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Q: 5. Suppose that X1, X2, ... , Xn are an iid sample from the distribution given below, f(X)e =…

A: Let X1,X2,...,Xn be a random sample of size n with probability density function(pdf) f(x) then the…

Q: Let X1, X2,...,X3 denote a random sample from a population having mean u and variance o2. 302 Which…

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Q: (a) Let X be a random variable and c is an arbitrary constant. Determine the value of c which makes…

A: Dear students as per guidelines we answer the first question only when multiple different question…

Q: Let X₁ and X₂ be the payoffs of two investments with E(X₁) = E(X₂) = 10. The expectation of the…

A: Given, X1 and X2 be the payoffs of two investments with EX1=EX2=10.

Q: For the simple linear model Y = a + BX + €, where the error variable e ~ independent of X, use the…

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Q: Show that if t" = (t+t) where t and ť are both most efficient estimators with variance v, then var…

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Q: If random variables X and Y each have variance o? = 3 and corr(X,Y) = 0.4, what is the value of…

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Q: If the RVSX1, X2, ..., Xn all have the same variance s and he correlation oxil ficient between each…

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Q: The probability of the joint event {x₁ < X ≤ x₂, Y₁ <Y ≤ y₂} is given as P{x₁ < X < x₂, Y₁ <Y ≤y₂} =…

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Q: 6. Let the random variables X and Y have the joint p.m.f. F(x,y) = 32 x+y x = 1, 2, y = 1,2,3,4.…

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Q: If X is a Poisson Variable such that P(X - 2) = 9 %3D P(X= 4 +90 P(X=6). Find the mean, variance and…

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Q: Example 10 : If X is a continuous random variable and Y = aX + b, prove that = a E(X) + b and V(Y) =…

A: It is given that Y=aX+b.

Q: For random variables X and Y such that E(X) = 2, E(Y) = 1, E(X²) = 10, E(Y²) = 3, and E (XY) %3D с,…

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Q: Let X1, X2, ..., X50 be 50 independent and identically distributed exponential random variables with…

A: As per bartleby guidelines, for more than three sub-parts, first three needs to be solved. Part (i)…

Q: Consider R.V. Y Unif (0, 1) What is the variance of U -4 In(Y)? %D

A: From the given information, Y~Unif0,1. f(y)=11-0      =1, 0&lt;y&lt;1

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.