If X ~N(µ=0,ơ=1), determine:
(a) Prob(X<-1.96)?
(b) Prob(X> 1.96)?
(c) Prob(-1.96<X< 1.96)
If X ~N(µ=0,ơ=1), determine: (a) Prob(X<-1.96)? (b) Prob(X> 1.96)? (c) Prob(-1.96<X< 1.96)
What is the confidence level for each of the following confidence intervals for µ? x ̅±1.96(δ⁄√n) x ̅±1.645(δ⁄√n) x ̅±2.575(δ⁄√n) x ̅±1.282(δ⁄√n) x ̅±0.99(δ⁄√n)
Find the DTFT a. x1[n]=(.3)^nµ[n] b. x2[n]=(.3)µ[n-1] c. x3[n]=(.3)^n(µ[n]-µ[n-10]) d. x4[n]=(.3)^n(µ[n-1]-µ[n-10]) e. x5[n]=δ[n] f. x6[n]=δ[n-1] g. x7[n]=δ[n]+3δ[n-1]+7δ[n-3]
5. A random variable X ∼ N (µ, σ2 ) is Gaussian distributed with mean µ and variance σ 2 . Given that for any a, b ∈ R, we have that Y = aX + b is also Gaussian, find a, b such that Y ∼ N (0, 1) Please show your work. Thanks!
Test Ho: µ =100; H1: µ < 100, using n = 36 and alpha = .05 If the sample mean=92 and the sample standard deviation = 18, which of the following is true? A. test statistic = -2.67; critical value = 1.69; we fail to reject Ho. B. test statistic = -2.67; critical value = 1.96; we fail to reject Ho. C. test statistic = -2.67; critical value = -1.96; we reject Ho. D. test statistic = -2.67; critical value...
Please send the detail solution ASAP
Assume X = [X1, X2, X3, X4]T ~ N(µ, C). Consider [1 2 2 6 7 8. µ = E[X] C= 3 7 11 12 4 8 12 16 o What is the pdf of px,(x) ? o What is the pdf of px1,X3(x1, 13) ? O Determine E[X2] ? O Determine E[X2 + X3] ? O Determine E[(X2 – X2)²] ? O Determine E[(X2 – X2)(X3 – X3)] ? O Determine E[X2X3] ?
X~N(-1,4). Find C so that Prob(miu - C < X <= miu + C) = 0.99 NOTE: WRITE YOUR ANSWER WITH 4 DECIMAL DIGITS. DO NOT ROUND UP OR DOWN.
Exercise5 Consider a linear model with n -2m in which yi Bo Pi^i +ei,i-1,...,m, and Here €1, ,En are 1.1.d. from N(0,ơ), β-(A ,A, β), and σ2 are unknown parameters, zı, known constants with x1 +... + Xm-Tm+1 + +xn0 , zn are 1, write the model in vector form as Y = Xß+ε describing the entries in the matrix X. 2, Determine the least squares estimator β of β.
Exercise5 Consider a linear model with n -2m in which...
4. Suppose thatz~N(0,1) (a) Find the probability that z >1. (b) Find the probability that zS-1.96. (c) Find the probability that 0>>-2. (d) Find the value之c such that there is a 90% probability that-2cくZく
Suppose X1, X2, . . . , Xn are i.i.d. Exp(µ) with the density f(x) = for x>0 (a) Use method of moments to find estimators for µ and µ^2 . (b) What is the log likelihood as a function of µ after observing X1 = x1, . . . , Xn = xn? (c) Find the MLEs for µ and µ^2 . Are they the same as those you find in part (a)? (d) According to the Central Limit...
Suppose X1, X2, . . . , Xn (n ≥ 5) are i.i.d. Exp(µ) with the density f(x) = 1 µ e −x/µ for x > 0. (a) Let ˆµ1 = X. Show ˆµ1 is a minimum variance unbiased estimator. (b) Let ˆµ2 = (X1 +X2)/2. Show ˆµ2 is unbiased. Calculate V ar(ˆµ2). Confirm V ar(ˆµ1) < V ar(ˆµ2). Calculate the efficiency of ˆµ2 relative to ˆµ1. (c) Show X is consistent and sufficient. (d) Show ˆµ2 is not consistent...