Find a probability density function f(x) for the distribution whose CDF is below. Make sure to beexplicit about the values of x for which your function is defined!F(x)3x31x<02x 0 < x <1x > 1

Let CDF = F(x) which is a Cumulative Distribution Function Let PDF = f(x) = Probability Density…

Answered: Find a probability density function…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...

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Let X be the number of years before a particular type of machines will need replacement. Assume that X has the probability function f(1) = 0.1, f(2) = 0.2, f(3) = 0.2, f(4) = 0.2, f(5) = 0.3. Find the probability that the machine needs no replacement during the first 3 years.
Explain why each option is true/false.
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Tossa coin once, S = (H,T) with P,(H) = p and P,(T) = q. Define X(-) by X(H) = ₁ X(T) = 0. Compute and plot the probability distribution function F, (x).
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A hospital is testing patients for Covid daily. The probability that a patient has covid is 34%. What is the probability that the 1st patient to test positive for covid will be found in the fifth test? Calculate V(X) and show distributions. show steps and work
The probability function for the number of insurance policies John will sell to a customer is given by f(x) = 0.5 for X = 6. 0, 1, or 2. (a) Is this a valid probability function? Explain your answer. Yes, f(x) 2 0 and Ef(x) + 1 Yes, f(x) > 0 and Ef(x) = 1 No, f(x) > 0 and Ef(x) # 1 No, f(x) > 0 and Ef(x) = 1 (b) What is the probability that John will sell exactly 2 policies to a customer? (Round your answer to three decimal places.) (c) What is the probability that John will sell at least 2 policies to a customer? (Round your answer to three decimal places.) (d) What is the expected number of policies John will sell? (Round your answer to three decimal places.) (e) What is the variance of the number of policies John will sell? (Round your answer to three decimal places.)
The annual rainfall in a certain country varies from 0 to 9 inches and is a random variable with probability density function defined by f(x): - 9.5 x 45 Find the following probabilities for the annual rainfall in a randomly selected year. Round your answers to 4 decimal places as needed. What is the probability that the annual rainfall is greater than 3 inches per year? What is the probability that the annual rainfall is less than 2 inches per year? What is the probability that the annual rainfall is between 2 and 4 inches per year?
There are 3 traffic lights on the way of the car. Each of them either permits or prohibits moving with the probability of 0.5. Let X be the number of traffic lights passed by the car before it stopped for the first time. (A) Write the probability distribution of X. (B) Find u(X), o(X), P(X = 1), P(X > 1).
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Battery life between charges for the Motorolla Droid Razr Maxx is 20 hours when the primary use is talk time. The battery life drops to 7 hours when the phone is primarily used for Internel applications over cellular. Assume that the battery life in both cases follows an exponential distribution. a. Show the probability density function for battery life for the Droid Razr Maxx phone when its primary use is talk time. b. What is the probability that the battery charge for a randomly selected Droid Razr maxx phone will last no more than 15 hours when its primary use is talk time? c. What is the probability that the battery charge for a randomly selected Droid Razr Maxx phone will last more than 20 hours when its primary use is talk time? d. What is the probability that the battery charge for a randomly selected Droid Razr Maxx phone will last no more than 5 hours when its primary use is Internet Applications?

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Find a probability density function f(x) for the distribution whose CDF is below. Make sure to be explicit about the values of x for which your function is defined! F(x) 3x3 1 x<0 2x 0 < x <1 x > 1