The random variable W has probability density function -{ = What is the cumulative probability function G(w) of W? g(w): 0 1 w < 1 w≥1
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Q: 1. What two properties must a function f that is a probability density function exhibit?
A: probability density function has two important properties . that are as follows
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- One of the important properties of the probability density function, f(x), of a random variable X is f(x) 2 0, for all values of X. Select one: O True O False PAGEThe probability density function for the continuous random variable X is given by: (A(x² – 2x + 2) 0Example 3: The probability density ƒ(x) of a continuous random variable is given by f(x) 3 ce , -mThe probability density function of a variate X is as follows, 1 2 3 4 P(X) k 3k 5k 7k 9k 11k 13k Find the value of, (i) k (ii) P(X < 4) (iii) P(3 < X < 6).A random variable has probability density function f(x) = 30x (1 - x) <(0 < xs 1). Compute its cumulative distribution F(x). O 10x3- 15x4 + 6x5 + 1 O 30x(1 - x) O 30x2 - 60x3 + 30x4 O 10x3 - 15x4 + 6x5 O none of these A Moving to the next question prevents changes to this answer. to search 63°F S End F10 Home %23 PrtScn F8 F2 F3 F4 F5 F6 F7 F9 近A continuous random variable has probability density function given by K(2x-3);1<x2 Find k if f(x) is a probability density functionThe probability density function for the continuous random variable X is given by: (А(х? — 2х + 21) 0A random variable X has the probability density function of the attached graph (see attached photo): a) What is the expected value of X? b) Compute P(-500 < X < -250).A shop receives a shipment of 1000 lamps. The probability that any individual lamp is defective is 0.2%. Assume the defectiveness is independent of cach lamp. Let X be the number of defective lamps in the batch of 1000. What is the probability mass function of X? O P(X = k) = (00) 0.002* (1 – 0.002)1000 , k = 0,1, 2, ..., 1000 O P(X = k) = 0.002* (1 – 0.002)1000–&, k = 0, 1, 2, .….., 1000 O P(X = k) = (1000) 0.002* (1 – 0.002)1000 , k = 1, 2, ..., 1000 O P(X = k) = (00)0.002100- (1 – 0.002)*, k = 0, 1, 2, ..., 1000The service life T (this year) of a particular type of electric toothbrush is assumed to have the probability density f given by: see figure question (a) Find the probability that a randomly selected toothbrush (of this type) has a lifespan of more than 2 years.(b) Assume that a toothbrush of the same type has been working for one year already. What is the probability that it works for at least another 3 years?(c) What is the probability that the average lifespan of T¯ for 90 independent toothbrushes is greater than 2.1 years?Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON