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.
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![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)
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- The probability density of a random variable X is given in the figure below. 1 From this density, the probability that X is at least 0.66 is:The table below shows an incomplete probability density function for X , the number of imperfections per batch of jeans that just came off a production line. What should the missing probability be? Provide the final answer as a decimal. x P(X = x) 0 0.88 1 0 2The table below represents the probability density function for the random variable X. Find the standard deviation of X. Round the final answer to two decimal places. x P(X = x) 1 1/4 3 1/4 4 1/2
- The random-number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a uniform probability distribution. (a) Identify the graph of the uniform density function. (b) What is the probability of generating a number between 0.48 and 0.62? (c) What is the probability of generating a number greater than 0.85? (a) Choose the correct graph of the uniform density function below. O A. O B. Density 1.2- 1- 0.8- 6. 0.6- 0 0.2 0.4 0.6 0.8 11.2 0.4- 0.2- to (b) The probability is (c) The probability is Q M (Simplify your answer.) (Simplify your answer.) ADensity 1.2- 1- 0.8- 0.6- 0.4- 0.2- to 0 0.2 0.4 0.6 0.8 1 1.2 Q M O C. 1.2- 1- 0.8- 0.6- 0.4- 0.2- Density 0+ 0 0.2 0.4 0.6 0.8 1 12 Q QFor a random variable which can be defined using the probability density function below, what is the probability that X is between 1.5 and 3.2? f(x) = {C(1+ x) ,1For a random variable which can be defined using the probability density function below, what is the probability that X is between 1.3 and 3.1? с (1 + х) ,1 <The table below represents the probability density function for the random variable X. Find the standard deviation of X. x P(X = x) 0 1/6 1 1/6 4 1/3 7 1/3The random-number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a uniform probability distribution. (a) Identify the graph of the uniform density function. (b) What is the probability of generating a number between 0.27 and 0.85? (c) What is the probability of generating a number greater than 0.92? (a) Choose the correct graph of the uniform density function below. A. B. Density 1.2- 1- 0.8- 606 0.6- 0.4- 0.2- 0 0.2 0.4 0.6 0.8 1 1.2 1.2- 1- 0.8- 0.6- 0.4- 0.2- 0+ Density X 0 0.2 0.4 0.6 0.8 1 1.2 (b) The probability is (c) The probability is to (Simplify your answer.) (Simplify your answer.) X C. 1.2- 1- 0.8- 0.6- 0.4- 0.2- Density 0 0.2 0.4 0.6 0.8 X 1 1.2Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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