5. Suppose Y has c.d.f. F(t) = 0, 1/6, 3/6, 1, for t < -1; for-1 < t < 2; for 2 ≤ t < 22; for t≥ 22. (a) Determine the p.m.f. or p.d.f. of Y, whichever is appropriate. (b) Recall that F(t) = P{Y ≤ t}. Define F(t-) by

5. Suppose Y has c.d.f. F(t) = 0, 1/6, 3/6, 1, for t < -1; for-1 < t < 2; for 2 ≤ t < 22; for t≥ 22. (a) Determine the p.m.f. or p.d.f. of Y, whichever is appropriate. (b) Recall that F(t) = P{Y ≤ t}. Define F(t-) by

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

5. Suppose Y has c.d.f.
F(t) =
0,
1/6,
3/6,
1,
for t < -1;
for −1≤ t < 2;
for 2 < t < 22;
for t > 22.
(a) Determine the p.m.f. or p.d.f. of Y, whichever is appropriate.
(b) Recall that F(t) = P{Y ≤ t}. Define F(t-) by
F(t) = lim F(t).
s-t
s<t
F(t) is the probability of what?
(c) What is F(t) – F(t−) the probability of?
(d) For F as given in this problem, what is F(21) – F(21–) and F(22) –
F(22-)?
(e) Let I be the interval defined by {t € R[F(t) ≥ 1/27}. The interval I is
of the form I = [b, ∞o) where b equals what?
(f) Let I be the interval defined by {t € R[F(t) ≥ 2/6}. The interval I is
of the form I = [b, ∞o) where b equals what?

Expert Solution

Step 1

From the given information,

The cdf of Y is,

$F (t) = \{\begin{cases} 0, f o r t < - 1 \\ \frac{1}{6}, f o r - 1 \leq t < 2 \\ \frac{3}{6}, f o r 2 \leq t < 22 \\ 1, f o r t \geq 22 \end{cases}$

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