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 more�