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onsider the following probability distribution function
Chapter , Problem 6.20(choose chapter or problem)
onsider the following probability distribution function for a continuous random variable: 3x2 f(x) = - -2 < x < 3 35 = 0 elsewhere (a) Show that this function satisfies the requirements of a probability distribution function. (b) Calculate the expected (mean) value of x. (c) Calculate the variance and the standard deviation of x.
Questions & Answers
QUESTION:
onsider the following probability distribution function for a continuous random variable: 3x2 f(x) = - -2 < x < 3 35 = 0 elsewhere (a) Show that this function satisfies the requirements of a probability distribution function. (b) Calculate the expected (mean) value of x. (c) Calculate the variance and the standard deviation of x.
ANSWER:Step 1 of 3
(a)
As given by the question,
There are given that the function
Now,
According to the concept of properties of the probability distribution, the sum of all possible probabilities must be equal to the 1.
So,
From the given function, the addition of a random value for x is 1.
Hence, the given function is satisfied for the probability distribution function.