### Assignment Instructions/ Description

Image transcription textProblem 1. True/False Questions

For questions (a)-(i), answer true or false. If you think a statement is false, explain why.

(a) You draw a random sample of size 500 from a Bernoulli distribution with parameter p and find that

the 95% confidence interval for p is [-0.43,0.57). If we draw another 100 random samples with size 500

from the same Bernoulli distribution with parameter p, we can expect that 95 of these intervals will

contain p.

(b) You draw a random sample of size 250 from a Geometric distribution with parameter p and construct

a 95% confidence interval for p. Your point estimate p for p calculated from your random sample is

always contained in the confidence interval.

(c) Suppose X ~ N(1, 2), i.e. X is normally distributed with mean 1 and variance 2. Markov's inequality

tells us that P(X 2 1) < 1.

Figure 1: p.d.f. of N(0, 0.5)

(d) Refer to Figure 1. P(X = 0) = 0.8.

(e) Suppose X1, X2. ..X,, have the following p.d.f,

fx. (x) =

7 (1 + x)2

for any real number x and i ( {1, 2, ..., n}. For any fixed e > 0, by the Weak Law of Large Numbers,

lim

1 -+ 0

P ( Ex - FIX, < < =1

for any j 6 {1, 2, ..., n}.

(f) Based on only the information in Table 1, we know that d(4.0) = 1.000.

(g) If X and Y are independent random variables, SD(X + Y) = SD(X) + SD(Y).

(h) Assume P(A) = 0.4 and P(B) = 0.5. Then, 0.5 < P(A UB) < 0.9.

(i) The following is a valid p.d.f,

-I

if - 1 <x <0

f(x) =

if 0 < x <1

otherwise... Show moreï¿½