a. Verify that the function given is a valid probability density function. b. Determine the cumulative density function (cdf) of the random variable X. c. Compute the probability that X is less than or equal to 0.5.
a. Verify that the function given is a valid probability density function. b. Determine the cumulative density function (cdf) of the random variable X. c. Compute the probability that X is less than or equal to 0.5.
Chapter9: Sequences, Probability And Counting Theory
Section9.7: Probability
Problem 1SE: What term is used to express the likelihood of an event occurring? Are there restrictions on its...
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Question
![Please answer the whole question quickly and
correctly
The probability density function (pdf) of a
continuous random variable X is given as follows:
a. Verify that the function given is a valid probability
density function.
b. Determine the cumulative density function (cdf)
of the random variable X.
c. Compute the probability that X is less than or
equal to 0.5.
d. Compute the probability that X is greater than or
equal to 1.5.
e. Compute the probability that X is between 0.5 and
1.5.
f. Compute the probability that X is exactly 0.5.
g. Compute the expected value of the random
variable X.
h. Compute the variance of the random variable X.
i. Find E[3X+4].
j. Find E[X2].
k. Find Var[-3X].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fabbd02aa-e289-47d3-b3b4-87f7eeaaef64%2F87b04248-af3a-4a9f-82ff-e5b59a2ce80a%2F4c649oq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Please answer the whole question quickly and
correctly
The probability density function (pdf) of a
continuous random variable X is given as follows:
a. Verify that the function given is a valid probability
density function.
b. Determine the cumulative density function (cdf)
of the random variable X.
c. Compute the probability that X is less than or
equal to 0.5.
d. Compute the probability that X is greater than or
equal to 1.5.
e. Compute the probability that X is between 0.5 and
1.5.
f. Compute the probability that X is exactly 0.5.
g. Compute the expected value of the random
variable X.
h. Compute the variance of the random variable X.
i. Find E[3X+4].
j. Find E[X2].
k. Find Var[-3X].
Transcribed Image Text:f(x) =
11--²
0
x<0
0<x< 1
2 1<x<2
x ≥ 2
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