1. Let X1,..., Xn, Y1,..., Yn be mutually independent ran- dom variables, and 1 Z = EX,Y;. n i=1 Suppose for each i e {1,...,n}, X; ~ Bernoulli(p), Y; ~ Binomial(n, p). What is Var[Z]?

Q: Find P (-1.5 < or equal to Z < 0.2) where Z ~ N (0,1)

A: We will use Standard Normal table to find the required probability.

Q: Consider an experiment Consting of independent rolls of a fair die, let W record the number f times…

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

Q: What is the devivative of |x|?

A: Our objective is to find the derivative of |x|.

Q: If X ~ N(5,2). Calculate P(X<6) [Draw a figure]

A:

Q: Rewrite the boolean expression in conjunctive normal form. 5. Determine whether or not the…

A:

Q: Suppose two cellphones are tested at random. We want to find out the number of defective cellphones…

A: Given information: There are 2 cellphones tested at random. D: The defective cellphones. N: The…

Q: Q2. | For what values of a, b and c does the function 6, x = 0 f(x) = {2x2 + a, bx + c, 0 <x < 2 2…

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Q: Let X~N(10,9).

A: The mean of the distribution is 10. The standard deviation of the distribution is 9.

Q: 10. If w is FALSE, x is TRUE, and y is FALSE, what is ((w OR Y') AND (x' AND y')') OR ((w OR y') AND…

A: Given :If w is FALSE, x is TRUE, and y is FALSE.To find : ((w OR y') AND (x' AND y')') OR ((w OR…

Q: The following data shows the death cases of COVID-19, x and the number of positive COVID-19 ca: y in…

A: Given data is

Q: 2. LetG = (Z12,) & H == {4,8,0}. Then [G:H]=3. *True *False

A:

Q: A survey of 200 shoppers was conducted to investigate how often people buy wine at a certain…

A: Introduction - Probability distribution of binomial distribution is given by  Px=nxpxqn-xwhere , P…

Q: (a) Let the interval a, b be divided into n equal sub-intervals such that a = x0 < a1 < x2 < x3…

A: From this general formula we can obtain different integration formulae by putting n=1, 2,3 etc. We…

Q: - - Find the largest number ♂ such that if |x − 1] < ɗ, then |2x − 2] < ɛ, where ɛ = 1. δς Repeat…

A: We will find the value of delta.

Q: 6. Let F = (-6, 5)U{-10, 10} U [7, 11). Find max F, min F, sup F, and inf F if they exist.

A:

Q: Let १ १G,१ी, (३,5) , (3 ), (4,2 ), ( 3 4) 5 %3D and 4. १,०) (2) (৬,), (,০), (3,) 3 %3D which of the…

A: The solution of the problem is given in the next step.

Q: 2. Suppose Y is G-measurable. Prove that Var(Y/G) = 0. %3D

A: Given that Y is G-measurable.

Q: Prove that if gcd (a,b)=1>then gcd (ab,ab)=l

A: I have proved using the fact that gcd can be expressed as integers linear combination q

Q: in in Signed-Rank Test a two-sided alternative, we may reject H0 in favor of H1 if either w+ or w-,…

A: Signed rank test for  two tailedHo:M≠Mowe reject Ho, if W+≤Wα and W-≤Wα

Q: Calculate the set op Convergence X72

A:

Q: How many more patients are recovered on Friday than Sunday? No of Covid cases admitted and recovered…

A: To find: How many more patients are recovered on Friday than Sunday.

Q: 6.) Derike the binomial idendity nent) (un-) C Hint: For mzz, c^)+2(^) +m?]

A: To derive the binomial identity22+42+62+.........+2n2=nn+14n-16

Q: A factory in Louisville, Kentucky, produces baseball bats. The diameter of the bat should be 9 cm.…

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Q: 6. If X is t-distributed, show that X² is F-distributed.

A:

Q: A business man goes 1 to the hotels X, Y,Z, , 20%, 50%, 30 % Of ttee time respecticely. Tt's kinown…

A: It is given that a men goes to a hotel X, Y, Z,  20%, 50% and  30% respectively, and there are 5%,…

Q: a random variable DA. Continuous O B. Continuous O C. None of thes O D. Discrete

A: The random variable represents all possible values of an outcome of the experiment. There are two…

Q: Find U4,, Ñ4, , if A, = {0,1, 2, .}, A2 = {2,3, ...}, ., An = {n,n+ 1,. %3D

A: For 1st part we have A1 U A2 U......An ={0,1,2,3,.........}

Q: Determine the numbers a such that x a (p) is solvable for p = 7, 11, and 13. %3D

A: Given, x3≡amod p At p=7 We know that suppose p is rational prime p≡1mod 3 then x3≡a mod p is…

Q: (3) Five balls are randomly selected without replacement from an urn with 11 black and 10 white…

A: Introduction: The random variable X is the number of black balls selected in the sample, when 5…

Q: A container contains 35 green​ tokens, 10 blue​ tokens, and 2 red tokens. Two tokens are randomly…

A: There are 35 green​ tokens, 10 blue​ tokens, and 2 red tokens. So total (35+10+2)=47 tokens.   Given…

Q: 4. For each positive integer i, let A, = {x € R| -<x < } = (-;;4) a. Find U-, A;. i=1 b. Find N 4:-…

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Q: Suppose that an ordinary deck of 52 playing cards will be randomly ordered, and then the cards will…

A: Given information: Given that the ordinary deck consists of 52 playing cards. The cards will be…

Q: A container contains 50 green​ tokens, 15 blue​ tokens, and 4 red tokens. Two tokens are randomly…

A: The container contains 50 green tokens, 15 blue tokens and 4 red tokens. So, there are 50 green…

Q: Suppose X is uniform on {6, 8, 10, 12, 14, 16}. What is Var[X]? A B C D E 27/12 33/12 35/12 35/3…

A: Solution-: Suppose X is uniform on {6,8,10,12,14,16} We want to find Var(X)=?

Q: The numbers a, b are positive integers. a ≤ b. Random variable X [2a,2b ] is the power of 2 in the…

A: From the given information, the numbers a and b are positive integers and a&lt;=b. The random…

Q: The result shows the person tested positive, what is the probability that the test is correct

A: Given that P(W1) = 0.10, P(W2) = 0.90 P(X | W1) = 0.80, P(X | W2) = 0.30

Q: 4. Which ones of the following functions are valid CDFs (all have x ≥ 0): (b) 1-exp(-) (0)1-exp(-)…

A: We are given the set of cumulative distribution functions .We have to choose which of the given…

Q: Ifx+y+z= 1 and x, y, z are positive, then show that ( 1)² ( 1)² ( 1)² 100

A: