9. IfX is a r.), distributed as N(μ, σ2), find the value of c (in terms...
2. Assume X is a random variable following from N(μ, σ2), where σ > 0. (a) Write down the pdf of X (b) Compute E(X2). (b) Define YFind the distribution of Y.
etX be normally distributed with mean μ = 120 and standard deviation σ = 20. (a) Find z such that P(X > z) = 0.90. (b) Find z such that P(80 S X 100).
Suppose that X1,X2, ,Xn are iid N(μ, σ2), where both parameters are unknown. Derive the likelihood ratio test (LRT) of Ho : σ2 < σ1 versus Ho : σ2 > σ.. (a) Argue that a LRT will reject Ho when w(x)S2 2 0 is large and find the critical value to confer a size α test. (b) Derive the power function of the LRT
Exhibit 9-1 n = 36 X 24.6 Ho: μ s 20 Hai μ>20 12 The p-value is O a. 2.1 O b..0107 c. .0214 d. .5107
IfX~ U(37,84), then P(X> 46|X<71) = 0.5319 0.8085 0.6923 0.7353
. (Ross 5.15) If X is a normal random variable with parameters μ-T0 and σ2-36, comput (a) P(X >5) (b) P(4 < X < 16) (c) P(X < 8) (d) P(X < 20) (e) P(X > 16)
8) Assume that X ~ N(μ = 4,02-1). Find c >0 such that P(-c 〈 X 〈 c) Find P(2 〈 X 〈 6) a. 0.95 b.
5.13. Suppose X1, X2, , xn are iid N(μ, σ2), where-oo < μ < 00 and σ2 > 0. (a) Consider the statistic cS2, where c is a constant and S2 is the usual sample variance (denominator -n-1). Find the value of c that minimizes 2112 var(cS2 (b) Consider the normal subfamily where σ2-112, where μ > 0. Let S denote the sample standard deviation. Find a linear combination cl O2 , whose expectation is equal to μ. Find the...
x-μ 6. Hint: use the formula*. If X falls within a range, transform both lower and upper limits. Let X be normally distributed with mean deviation σ 4 a. Find P(X30). b. Find P(X> 2), c. Find P(4 <X< 10). d. Find P(6 <X< 14) 10 and standard
The probability mass function of a random variable X is given by Px(n)r n- (a) Find c (Hint: use the relationship that Ση_0 n-e) (b) Now assume λ = 2, find P(X = 0) (c) Find P(X>3)