3.4. The probability density function of the random variable X is given as follows. fx(x) = cx =0 0≤ x ≤ 1 otherwise a) What should be the value of c so that fx(x) is a proper probability density function? b) Plot the function fx(x). c) Compute E(X), median and mode of X. d) Compute the variance, standard deviation and coefficient of variation of X. 3.5. Prove Theorem 3.7. 3.6. The random variable X takes the value of 5 with a probability of 0.30 and has a triangular distribution in the range [0, 20] as shown in the following figure (Fig. 3.6). a) What should be the value of the coefficient k so that X has a valid probability density function? Write down the equation that specifies the probability distribution of X. b) Find the mean, median and mode values of X. c) Find the variance, standard deviation and coefficient of variation of X. d) If it is known that X will not get a value greater than 15, what is the probability that X will be greater than 12?
3.4. The probability density function of the random variable X is given as follows. fx(x) = cx =0 0≤ x ≤ 1 otherwise a) What should be the value of c so that fx(x) is a proper probability density function? b) Plot the function fx(x). c) Compute E(X), median and mode of X. d) Compute the variance, standard deviation and coefficient of variation of X. 3.5. Prove Theorem 3.7. 3.6. The random variable X takes the value of 5 with a probability of 0.30 and has a triangular distribution in the range [0, 20] as shown in the following figure (Fig. 3.6). a) What should be the value of the coefficient k so that X has a valid probability density function? Write down the equation that specifies the probability distribution of X. b) Find the mean, median and mode values of X. c) Find the variance, standard deviation and coefficient of variation of X. d) If it is known that X will not get a value greater than 15, what is the probability that X will be greater than 12?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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