13-17. If a random variable X assumes the values 0 and 1 with P(X= 0) = 3 P(X = 1), then nX) is: (ii) i6 (iii) i6 (iv) 음
Q: 4. (a) Consider a nonnegative, integer valued random variable Y, and a random sample X1, ·.. , Xn.…
A: Expectation gives the most likely value of a random variable.
Q: Suppose X is a random variable such that EX = 50 and V arX = 12. Find (a) E(X 2 ) (b) E(3X + 2) (c)…
A: The given X is a random variable with EX=50 and VarX=12.
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Q: Q11 If the random variable x as a mean of μ and a variance of o² What is the P(x-μ)² <20)= a) less…
A: Chebyshev's inequality has used to find the probability.
Q: 3- , thei a) E{f,(y\x)} =- exp(- o/27(2-r²) 20ʻ(2-r²)' 1 b) E{f, (x)f;(y)}=- 2.noV4-r
A:
Q: (1) Let X be a random variable with a function [A(3x² +6) -1,0,1,2 . then (0) k = (6) k = (e) * (d)…
A:
Q: 8. Two independent random variables X1=(-1.0.1) and X2-(0.1) can take the following probability…
A: Expected value is used for discrete or continuous probability function. It is calculated by the…
Q: 20.21. Suppose that the sequence (X) is fundamental in probability in the sense that for e positive…
A: Given: PXm-Xn>∈<∈ for m,n >Ne
Q: ) Let X be a random variable with p.d.f.
A: It is an important part of statistics. It is widely used.
Q: 3 The random variable X ~ B(40, 0.4). Find: a P(X 16) e P(11< X< 15) d P(10< X< 17)
A: The mean is computed as: The standard deviation is computed as In the given case, the required…
Q: 4. Let X be a random variable taking positive values and assume that E(X) exists. Which of the…
A: Option (I) is correct as E(X2)>= (E(X))2 when we find Variance.
Q: Two random variables X and Y have joint char- acteristic function yl@,m)=exp(-2@,² – 80;) (i) Show…
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Q: 1+3x 1-4x (10) If a random variable assumes 4 values with probability 1+1 1+2 and the condition on x…
A: A random variable assumes 4 values with probability p1=1+3x4 , p2=1-x4 , p3=1+2x4 , p4=1-4x4
Q: 1-4x and 4 1+3x 1-x 1+2x (5) If a random variable assumes 4 values with probability the 4 4 4…
A: If the random variable assumes 4 values , then the sum of all probabilities for x should be equal to…
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Q: Gaussian random variables X₁ and X₂ whose X₁ = 2,0x²=9₁ X₂ =−1, 2 = 4 and Cx₁x=-3 are transformed to…
A:
Q: (33) Let X be a random variable with p.d.f. e2k x= 1,2,3 f(x)=- find (1) k (2) E(x+1) O.W
A: Given that X is a random variable with p.d.f f(x)=e2k ; x=1,2,30 ; Otherwise.
Q: (2) Let X be a random variable with p.d.f. 1<x<10 f(x) = then o.w 3 (a) k=2 (b) k=8 (c) k = (d) k=3…
A: Solution: 2. From the given information, the probability density function of X is
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Q: 4. Suppose X is a random variable such that E( 3X - 7) = 8 and E() 19. What is Var( 70 – 2X ) ?
A: We have, E(3X-7)=8⇒3E(X)-7=8⇒3E(X)=15⇒E(X)=153=5 Also, E(X22)=19⇒E(X2)=19×2=38 Then,…
Q: Question * Suppose that X and Y are random variables with E(X) = 2. E(Y) = 5 and E(X²) = 8, E(Y) =…
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Q: 8. IFX is a continuous random variable and y = ax + b then the expected valued of y = ? a. aE(x) b.…
A: y=ax+b
Q: Let X and Y be random variables with joint distribution pxy(:) given by the following table. Pxy X =…
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Q: (5) If X is a normal N(0, 1) random variable then E(X) is 1 -1 N/A (Select One) (6) Find the…
A: (5) If X is a normal N0,1 random variable. That is, μ=0,σ2=1. The expected value of X is, μ=EX=0…
Q: 1. Suppose X~ N(₁,02), i = 1,..., n are independent random variable State the distribution of each…
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Q: If random variable X is such that E[(X-1)]=10, E[(X-2)] = 6, what is σ'
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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: (1) Let X be a random variable with p.d.f. e 0<x<0 k ƒ(x) = < find k. O.W
A: Let X be a random variable with pdf fx=1ke-8x 0<x<∞0 otherwise…
Q: Given that X is a random variable with E(X²) = 16 and Var(X)= 7; find E(X). (A) 9 (B) V3 (C) 3 (D)…
A:
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- The probability generating function for a random variable X is given by: 1 1,25 1 9x(z) =z2 + 1 -z20 710 + 2 P(X < 5 |X < 13) equals Select one: а. 0.8 b. 0.2 C. 1 d. 0.286 е. ОLet random variable X be the number of users communicating with a cellular base station within a given time interval. Its PMF is :3. Let X be the random variable that takes on the integers {0, 1, 2, ..., 15} with equal probabilities. Define a new random variable Y = X + A, where A is a random variable that takes on the values {-1, 0, 1} with equal probabilities. If the RVs X and A are independent, find the mutual information between X and Y.
- 20Let Z be a random variable with E(Z) = 12 and Var(Z) = 5. Based on the statement above, determine which of the following statements are true and false. Show complete solution. a) E(3Z + 10) = 46 b) E(Z^2) = 160 c) Var(10)=10(3) Let X be a random variable with p.d.f. 2k 3x f(x)= I9. If X and Y are two random variables and let g(X) be a random variable. Show that (a) E[g(X) X=x] = g(x). (b) E[g(x)Y|X=x] = g(x) E[Y|X=x]. Assume that E[g(x)] and E[Y] exist.(1) Let X be a random variable with p.d.f. ke 3 01. Given that X~N(39,32)A Random variable X is normally distributed and has a mean of 9 C Random variable X is not normally distributed and the mean is 39 B Random variable X is normally distributed and has a mean of 3 D Random variable X is normally distributed and the mean is 3924. Gaussian random variables X, and X,, for which, X, = 2, o = 9, X, =-1, ox, = 4 and Cxx, =-3, are transformed to new random variables Y, and Y, according to जापर डेरें| Y, =-X, + X, Y, =-2X,- 3X, (iii) Cy,Cy, .. Find(1) Let X be a random variable with a function k(3x2 +6) f(x) =- -1,0,1,2 then O.w 1 1 1 (a) k = 44 (b) k =- 43 7 (c) k = 42 (d) k (e) None of these 44 a is the correct answer b is the correct answer O c is the correct answer d is the correct answer e is the correct answer4 of these 1 5 of these 3 of (a) 1.0211 (c) 1.5207 (e) 1.2962 these 2 (a) 0.1111 (c) 2.3333 (e) 12.9375 2 of these 16 tickets total 3 FIG. 5. 2 of these 26. Let X be the random variables described in Fig- ure 5. Find E(√x + 1). (b) 2.3125 (d) 0.4613 X Random draw from the box 27. Let X be the random variable described in Figure 5. Find E(X³ | X < 2). (b) 0.5625 (d) 1.3125SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON