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CPoisson can not be determined. distribution P(np) ) Suppose X~N(0,1) and YN(24), they are independent, then...
3) Suppose X,,X,,X, (n > 1) is a random sample from Bernoulli distribution with Circle out...
3) Suppose X,,X,,X, (n > 1) is a random sample from Bernoulli distribution with Circle out your Class: Mon&Wed or Mon.Evening p.mf. p(x)=p"(I-p)'-x , x = 0,1, , thenyi follows ( ). Binomial distribution B(a.p) eNormal distribution N(p,mp(- O Poisson distribution P(np) Dcan not be determined. 4) Suppose X-N(0,1) and Y~N(24), they are independent, then )is incorrect. X+Y N(2, 5) C X-Y-NC-2,5) BP(Y <2)>0.5 D Var(X) < Var(Y) x,X,, ,X, (n>1) is a random sample from N(μσ2), let-1ΣΧί 5) Suppose...
3) Suppose X~N(0,1) and Y~N(2,4), they are independent, then is incorrect. 6 X-Y N(-2,5) D Var(X)...
3) Suppose X~N(0,1) and Y~N(2,4), they are independent, then is incorrect. 6 X-Y N(-2,5) D Var(X) < Var(Y) SupposeX-N(Aof) and Y-N(H2,σ ), they arc indcpcndcnt, thcn in the following statementss incorrect 4) 5) Suppose X~NCHiof) and Y~NCHz,σ ), they are independent, if PCIX-Hik 1) > PCIY _ μ2I 1), then ( ) is correct.
3) SupposexxX () is a random sample from Bernoulli distribution wi Qwestlon pmL p(x) = p,...
3) SupposexxX () is a random sample from Bernoulli distribution wi Qwestlon pmL p(x) = p, (l-p)'-. , x-0,1, . then follows ( ). ndividual was cie ANormal distribution N(np,np(a-p) D Binomial distribution Bin.p) Dean not be determined. Poisson distribution P(np) (1). Fimd a,suc (2) Write out d uppose X~NCO,1) and Y-NC2.4), they are independent, then is incorrect. expected am X + Y-N(2, 5) X-Y-N(-2,5) ⓝPCY < 2) > 0.5 DVarx) Vary is a random sample from N(H, let x...
ppolt & Taluom Variable has edf. F(x), then the probability that X lies in the interval...
ppolt & Taluom Variable has edf. F(x), then the probability that X lies in the interval [a, b) is Question 2. 30 pt.) Single-choice questions 1) Suppose A and B are independent events, then)is incorrect. P(AIB) = P(A) B P(AB)- P(A) D PCA u B) = P(A) + P(B) e P(A B)-P(A)P(B) 2) Suppose X-Bin(10,0.3) and Y-Bin(15,0.3), they are independent, thenis incorrect. oX+Y-Bin(25,0.3) GX+Y-N(7.5,5.25) D VarX)VarCr) 3) Suppose X N(0,1) and YN(2,4), they are independent, then is incorrecet X +...
4. Suppose Yi, Yn are iid randonn variables with E(X) = μ, Var(y)-σ2 < oo. For...
4. Suppose Yi, Yn are iid randonn variables with E(X) = μ, Var(y)-σ2 < oo. For large n, find the approximate distribution of p = n Σηι Yi, Be sure to name any theorems you used.
Question 3: A random variable X has a Bernoulli distribution with parameter θ є (0,1) if...
Question 3: A random variable X has a Bernoulli distribution with parameter θ є (0,1) if X {0,1} and P(X-1)-θ. Suppose that we have nd random variables y, x, following a Bernoulli(0) distribution and observed values y1,... . Jn a) Show that EIX) θ and Var[X] θ(1-0). b) Let θ = ỹ = (yit . .-+ yn)/n. Show that θ is unbiased for θ and compute its variance. c) Let θ-(yit . . . +yn + 1)/(n + 2) (this...
Let Z ~ N(0,1) and let Y = Z2. Find the distribution of Y. Hint: Use...
Let Z ~ N(0,1) and let Y = Z2. Find the distribution of Y. Hint: Use moment generating function. Let X ~ N(j = 1, 02 = 4). If Y = 0.5*, find E(Y?). Hint: Use moment generating function.
Let X have the pdf defined for 0<x<2. Let Y~Unif(0,1). Suppose X and Y are independent....
Let X have the pdf defined for 0<x<2. Let Y~Unif(0,1). Suppose X and Y are independent. Find the distribution of X-Y. fx() =
2 Expectation, Co-variance and Independence [25pts + 5pts] Suppose X, Y and Z are three different...
2 Expectation, Co-variance and Independence [25pts + 5pts] Suppose X, Y and Z are three different random variables. Let X obeys Bernouli Distribution. The probability disbribution function is s 0.5 x=c 0.5 x= -c. c is a constant here. Let Y obeys the standard Normal (Gaussian) distribution, which can be written as Y ~ N(0,1). X and Y are independent. Meanwhile, let Z = XY p(x) = { 0.5 • Are Y and Z independent? (Just clarify) [3pts] • Show...
12. Let X and Y be independent random variables, where X has a uniform distribution on the interval (0,1/2), and Y...
12. Let X and Y be independent random variables, where X has a uniform distribution on the interval (0,1/2), and Y has an exponential distribution with parameter A= 1. (Remember to justify all of your answers.) (a) What is the joint distribution of X and Y? (b) What is P{(X > 0.25) U (Y> 0.25)}? nd (c) What is the conditional distribution of X, given that Y =3? ur worl mple with oumbers vour nal to complet the ovaluato all...
3) Suppose X,,X,,X, (n > 1) is a random sample from Bernoulli distribution with Circle out your Class: Mon&Wed or Mon.Evening p.mf. p(x)=p"(I-p)'-x , x = 0,1, , thenyi follows ( ). Binomial distribution B(a.p) eNormal distribution N(p,mp(- O Poisson distribution P(np) Dcan not be determined. 4) Suppose X-N(0,1) and Y~N(24), they are independent, then )is incorrect. X+Y N(2, 5) C X-Y-NC-2,5) BP(Y <2)>0.5 D Var(X) < Var(Y) x,X,, ,X, (n>1) is a random sample from N(μσ2), let-1ΣΧί 5) Suppose...
3) Suppose X~N(0,1) and Y~N(2,4), they are independent, then is incorrect. 6 X-Y N(-2,5) D Var(X) < Var(Y) SupposeX-N(Aof) and Y-N(H2,σ ), they arc indcpcndcnt, thcn in the following statementss incorrect 4) 5) Suppose X~NCHiof) and Y~NCHz,σ ), they are independent, if PCIX-Hik 1) > PCIY _ μ2I 1), then ( ) is correct.
3) SupposexxX () is a random sample from Bernoulli distribution wi Qwestlon pmL p(x) = p, (l-p)'-. , x-0,1, . then follows ( ). ndividual was cie ANormal distribution N(np,np(a-p) D Binomial distribution Bin.p) Dean not be determined. Poisson distribution P(np) (1). Fimd a,suc (2) Write out d uppose X~NCO,1) and Y-NC2.4), they are independent, then is incorrect. expected am X + Y-N(2, 5) X-Y-N(-2,5) ⓝPCY < 2) > 0.5 DVarx) Vary is a random sample from N(H, let x...
ppolt & Taluom Variable has edf. F(x), then the probability that X lies in the interval [a, b) is Question 2. 30 pt.) Single-choice questions 1) Suppose A and B are independent events, then)is incorrect. P(AIB) = P(A) B P(AB)- P(A) D PCA u B) = P(A) + P(B) e P(A B)-P(A)P(B) 2) Suppose X-Bin(10,0.3) and Y-Bin(15,0.3), they are independent, thenis incorrect. oX+Y-Bin(25,0.3) GX+Y-N(7.5,5.25) D VarX)VarCr) 3) Suppose X N(0,1) and YN(2,4), they are independent, then is incorrecet X +...
4. Suppose Yi, Yn are iid randonn variables with E(X) = μ, Var(y)-σ2 < oo. For large n, find the approximate distribution of p = n Σηι Yi, Be sure to name any theorems you used.
Question 3: A random variable X has a Bernoulli distribution with parameter θ є (0,1) if X {0,1} and P(X-1)-θ. Suppose that we have nd random variables y, x, following a Bernoulli(0) distribution and observed values y1,... . Jn a) Show that EIX) θ and Var[X] θ(1-0). b) Let θ = ỹ = (yit . .-+ yn)/n. Show that θ is unbiased for θ and compute its variance. c) Let θ-(yit . . . +yn + 1)/(n + 2) (this...
Let Z ~ N(0,1) and let Y = Z2. Find the distribution of Y. Hint: Use moment generating function. Let X ~ N(j = 1, 02 = 4). If Y = 0.5*, find E(Y?). Hint: Use moment generating function.
2 Expectation, Co-variance and Independence [25pts + 5pts] Suppose X, Y and Z are three different random variables. Let X obeys Bernouli Distribution. The probability disbribution function is s 0.5 x=c 0.5 x= -c. c is a constant here. Let Y obeys the standard Normal (Gaussian) distribution, which can be written as Y ~ N(0,1). X and Y are independent. Meanwhile, let Z = XY p(x) = { 0.5 • Are Y and Z independent? (Just clarify) [3pts] • Show...
12. Let X and Y be independent random variables, where X has a uniform distribution on the interval (0,1/2), and Y has an exponential distribution with parameter A= 1. (Remember to justify all of your answers.) (a) What is the joint distribution of X and Y? (b) What is P{(X > 0.25) U (Y> 0.25)}? nd (c) What is the conditional distribution of X, given that Y =3? ur worl mple with oumbers vour nal to complet the ovaluato all...
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