5)Given the function0 < x < bfx(x) =elseFor the function to be vaild probability density, the constant b > 01In(13)а.b. In(2)c. In(16)d. - In(12)

The function is said to be valid probability density if the integration of f(x) over whole range is…

Answered: Given the function 0 0

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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In Minecraft, about 5 zombies will spawn every minute. Define X as the waiting time in minutes for the first zombie to spawn. The probability density function is then given by f (x) = 0, x > 0 x < 0 Find the CDF, F(x). Write your answer as a piecewise function.
3. The percent of people who will attend an event and not cancel their reservation has a probability density function given by (a) f(x) = {or Determine the value of the constant, a. ar³ (1-1), 0≤ I ≤ 1, otherwise. (b) The cost of a ticket is $100, and anybody who cancels their reservation will receive a full refund. The total cost of hosting the event will be $10,000. What is the minimum number of tickets that should be sold so that the expected profit is $12,000. (c) Suppose the number of tickets sold is the same as in your previous answer. What would be the variance in the profit?
2. Let X have the probability density function: 10-12². √x f(x) = a. What is a? b. What is E(X)? C. What is Var(X)? 0, 0≤x≤ a otherwise
2. Consider a gas station's daily sales. Let Y be the volume of gas sold per day in 1000s of gallons. Assume the distribution of Y follows this pdf: 1sxs 2 S (v) . else What value of k is required for the above function to be a valid pdf? b. Verify that the function given is a valid probability density а. function c. Determine the cumulative distribution function (cdf) of the random variable d. Compute the probability that there is exactly 1500 gallons of sales on a given day (Hint: Find?(r - 1.5)) = 1 CO0
Q2. The probability density function of X is as follows. f(x) = 2 - 2x, for x = [0, 1] Which one of the following expressions can be used to find P(0.5 < X < 1.5)? F(x) is the cumulative distribution function of X. (A) 1 - F(0.5) (C) F (1.5)-f(0.5) (B) f(1.5)-f(0.5) (D) 1.5 (2 - 2x) dx (E) other
A continuous random variable, X, has the following probability density function. k cos for 0sxs1 f(x)=- for all other values of x (a) Show that k = Find p( x sxs). (b) (c) Find the median of X.

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