It has been reported that men are more likely than women to participate in online auctions. In a recent survey, 65% of responde
1 answer:
Answer:
0.84 or 84%
Step-by-step explanation:
Let 'n' be number of people who took the survey, the number of men who answered the survey is 0.45n. The number of men who answered the survey and have participated in online auctions is 0.38n. Therefore, choosing from the population of men who took the survey (0.45n) the probability that a respondent had participated in an online auction is:
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The solutions to the questions are
- The probability that X is between 2 and 4 is 0.314
- The probability that X exceeds 3 is 0.199
- The expected value of X is 2
- The variance of X is 2
The probability density function is given as:
f(x)= xe^ -x for x>0
The probability is represented as:
So, we have:
Using an integral calculator, we have:
Expand the expression
Evaluate the expressions
P(2 < x < 4) =-0.092 +0.406
Evaluate the sum
P(2 < x < 4) = 0.314
Hence, the probability that X is between 2 and 4 is 0.314
<h3>Find the probability that the value of X exceeds 3</h3>This is represented as:
Using an integral calculator, we have:
Expand the expression
Evaluate the expressions
P(x > 3) =0 + 0.199
Evaluate the sum
P(x > 3) = 0.199
Hence, the probability that X exceeds 3 is 0.199
<h3>Find the expected value of X</h3>This is calculated as:
So, we have:
This gives
Using an integral calculator, we have:
Expand the expression
Evaluate the expressions
E(x) = 0 + 2
Evaluate
E(x) = 2
Hence, the expected value of X is 2
<h3>Find the Variance of X</h3>This is calculated as:
V(x) = E(x^2) - (E(x))^2
Where:
This gives
Using an integral calculator, we have:
Expand the expression
Evaluate the expressions
E(x^2) = -0 + 6
This gives
E(x^2) = 6
Recall that:
V(x) = E(x^2) - (E(x))^2
So, we have:
V(x) = 6 - 2^2
Evaluate
V(x) = 2
Hence, the variance of X is 2
Read more about probability density function at:
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<u>Complete question</u>
A random variable X with a probability density function f(x)= xe^ -x for x>0\\ 0& else
a. Find the probability that X is between 2 and 4
b. Find the probability that the value of X exceeds 3
c. Find the expected value of X
d. Find the Variance of X