Isd (m, n) = 1 and p|m then gcd (n, p) = 1

Q: 5. (i) If gcd(a, b) = 1 and c| (a + b), then ged(a, c) = 1 and gcd(b, c) = 1. (ii) If ged(a, b) = 1…

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Q: Inside of a jar are four balls that are labeled 1, 2, 3, and 4. You randomly choose three balls from…

A: Basic Probability: You should be familiar with fundamental concepts of probability, such as sample…

Q: 2. Let A = 201-18 and /= 2 1 1 2 01 Find A(A+1).

A: A=[2 1      1 2]I=[1 0      0 1]

Q: P (A) a, P (B) b and P (P (AB)- c then the expression of P (A'B')in erms of a, b and c is:

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Q: In PCA, we obtain z E Rk from x E R" as follows: T z = u(1) y(2) u(k) Which of the following is a…

A: Given that,In PCA, we obtain z∈Rk from x∈Rn as follows:z=|u(1)| |u(2)| ...…

Q: Prove that P (a SX< b) = Fx (b) -Fx (a)

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Q: Q.2 Find the probability generating function of :1) P(X=2n) 2) P(X<n).

A: If X and Y are non-negative independent integral valued discrete random variables with respective…

Q: Show that gcd(a, bc) = 1 if and only if gcd(a, b) = 1 and gcd(a, c) = 1.

A: Consider, gcd(a, b) =1 and gcd(a, c) = 1. If gcd(a, b) =1 then there exist integers m and n such…

Q: (2x-x*), 2x-x²), 0<xs2 Suppose X is random variable whose p.d.f. is f(x)={4 0, elsewhere Find the…

A: It is an important part of statistics. It is widely used.

Q: Show Mat Res (r(z), -n) (1)" n!

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Q: 3. Let the random variable X have the pmf f(x) = = a) E(X) b) E(X²) c) E(3X²2X + 4) (x+1)² for x =…

A: The provided information is as follows:The probability mass function of  is .

Q: The probability of success in a certain game is p. The results in successive trials are independent…

A: Let random variable X be the number of trials performed before r successes are obtained. Then the…

Q: A container contains 35 green tokens, 5 blue tokens, and 3 red tokens. Two tokens are randomly…

A: There are total (35+5)=40 non-red tokens and 3 red tokens in the container.  And total (35+5+3)=43…

Q: Let X ∼ N ( 1 , 4 ) and Y ∼ N ( 2 , 9 )be independent and let W = X2 +2Y + 3. Then what is the mean…

A: Given, Therefore,

Q: Prove that gcd(k; n) = gcd(n - k,n).

A: Greatest common divisor (gcd) :            If a , b are two integers such that atleast one different…

Q: For events A, B, and C, we have the following probabilities: P(A) 0.7, P(B) = 0.5, P(C) = 0.3, P(A…

A:

Q: show all solution 1. Suppose X is a random variable with E(X2)=10 and E(X)=2. Find the following:…

A: Variance of constant is 0.

Q: If gcd( m,91) = gcd(n, 91) = 1 %3D %3D

A: Given, if gcd(m, 91)=gcd(n, 91)=1,  To prove that                     91|m37-n37

Q: Prove gcd(n, n+1) = 1.

A: To prove the below expression. gcdn, n+1=1

Q: (iii) If gcd(a, b) = 1 and a | bc, then a | c.

A: In the given question, concept of Greatest Common divisor is applied. Greatest Common divisor The…

Q: 3 dr. (1)

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Q: Random variables X and Y are connected through pgf ¤x(s) and Vy(s) by the relation x(s) = s¥y(/s)…

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Q: (a) P( W=2 | Z = 1) (b) P( Z=0 | W = 1) ; (c) are Z and W independent?

A: Here make joint distribution table

Q: Show that C(2n, n)+C(2n, n−1)= 1/2C(2n+2, n+1).

A: We have to show that:

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Q: If gcd(m,n) = 1 then (a) lcm(m, n) = 1 (b) gcd(m³,n³) = 1 (c) cd(m +n,m– n) = 1 (d) None of these

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Q: b (x, n, 1-p) =

A: The expression is b(x, n, 1-p).

Q: Let P(C) = 0.3• Let P(D) = 0.8• Let P(C|D) = 0.3 A. P(C AND D) = [ Select ]  ["0.30", "0.24",…

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

Q: I roll a die with 10 faces numbered 0-9 and obtain a score X. What is E(X)?

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