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Question 5 The continuous random variable X has cumulative distribution function given by: F(x) = { 0, x < 2, 1/5(x^2 - 4), 2 ? x ? 3, 1, x > 3. Find the probability density function, f(x). Question 6 The continuous random variable X has cumulative distribution function given by: F(x) = { 0, x < 1, 1/2(x - 1), 1 ? x ? 3, 1, x > 3. a Find P(X ? 2.5). b Find P(X > 1.5). c Find P(1.5 ? X ? 2.5). Question 7 The continuous random variable X has probability density function given by: f(x) = { 3x^2/8, 0 ? x < 2, 0, otherwise. a Find the cumulative distribution function of X. b Find P(X ? 1).

          Question 5
The continuous random variable X has cumulative distribution function given by:
F(x) = {
0, x < 2,
1/5(x^2 - 4), 2 ? x ? 3,
1, x > 3.
Find the probability density function, f(x).

Question 6
The continuous random variable X has cumulative distribution function given by:
F(x) = {
0, x < 1,
1/2(x - 1), 1 ? x ? 3,
1, x > 3.
a Find P(X ? 2.5).
b Find P(X > 1.5).
c Find P(1.5 ? X ? 2.5).

Question 7
The continuous random variable X has probability density function given by:
f(x) = {
3x^2/8, 0 ? x < 2,
0, otherwise.
a Find the cumulative distribution function of X.
b Find P(X ? 1).

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Question 5
The continuous random variable X has cumulative distribution function given by:
F(x) =
0, x < 2,
1/5(x^2 - 4), 2 ? x ? 3,
1, x > 3.
Find the probability density function, f(x).

Question 6
The continuous random variable X has cumulative distribution function given by:
F(x) =
0, x < 1,
1/2(x - 1), 1 ? x ? 3,
1, x > 3.
a Find P(X ? 2.5).
b Find P(X > 1.5).
c Find P(1.5 ? X ? 2.5).

Question 7
The continuous random variable X has probability density function given by:
f(x) =
3x^2/8, 0 ? x < 2,
0, otherwise.
a Find the cumulative distribution function of X.
b Find P(X ? 1).

Added by Suzanne G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Lucas Finney

11/16/2022

Step 1

So, we differentiate F(x) with respect to x to get f(x). For the given F(x), we have: f(x) = { 0, x < 2 1/2(x-2), 2 ≤ x < 3 0, x ≥ 3 } Question 6: For F(x) = { 0, x < 4 1/6(x-4)^3, 4 ≤ x < 6 1, x ≥ 6 }, we have: F(X < 2.51) = 0, because 2.51 is less than 4. Show more…

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Question 5 The continuous random variable X has cumulative distribution function given by: F(x) = { 0, x < 2, 1/5(x^2 - 4), 2 ≤ x ≤ 3, 1, x > 3. Find the probability density function, f(x). Question 6 The continuous random variable X has cumulative distribution function given by: F(x) = { 0, x < 1, 1/2(x - 1), 1 ≤ x ≤ 3, 1, x > 3. a Find P(X ≤ 2.5). b Find P(X > 1.5). c Find P(1.5 ≤ X ≤ 2.5). Question 7 The continuous random variable X has probability density function given by: f(x) = { 3x^2/8, 0 ≤ x < 2, 0, otherwise. a Find the cumulative distribution function of X. b Find P(X ≤ 1).

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