a.
Find
a.
Answer to Problem 11SE
The value of
Explanation of Solution
Given info:
The probability density
Calculation:
The value of
Thus, the value of
b.
Find the probability that both fuses last at least 3 years.
b.
Answer to Problem 11SE
The probability that both fuses last at least 3 years is 0.0821.
Explanation of Solution
Calculation:
The probability that both fuses last at least 3 years represents the
The value of
Thus, the probability that both fuses last at least 3 years is 0.0821.
c.
Find the marginal probability density functions of X.
c.
Answer to Problem 11SE
The marginal probability density functions of X is,
Explanation of Solution
Calculation:
The formula for finding marginal probability density function
The marginal probability density function
For
Here,
Therefore,
For
Here,
Therefore,
Thus, the marginal probability density functions of X is,
d.
Find the marginal probability density functions of Y.
d.
Answer to Problem 11SE
The marginal probability density functions of Y is,
Explanation of Solution
Calculation:
The formula for finding marginal probability density function
The marginal probability density function
For
Here,
Therefore,
For
Here,
Therefore,
Thus, the marginal probability density functions of Y is,
e.
Explain whether X and Y are independent or not.
e.
Answer to Problem 11SE
Yes, X and Y are not independent because
Explanation of Solution
Calculation:
If
Here,
Thus, X and Y are independent.
Want to see more full solutions like this?
Chapter 2 Solutions
Statistics for Engineers and Scientists
- Show that each function defined as follows is a probability density function on the given interval; then find the indicated probabilities. f(x)=(1/2)ex/2;[0,) a. P(0X1) b. P(1X3) c. P(X2)arrow_forwardShow that each function defined as follows is a probability density function on the given interval; then the indicated probabilities. f(x)=12(1+x)3/2;[0,) a. P(0X2) b. P(1X3) c. P(X5)arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,