The random variable Y has a probability density function that is equal to c. e* when x > -1 and 0 when x < -1 for some positive constant c. What is the probability P(Y ≤ 2)? O 03 -3 01-e ³ 1-e-2 е 01-e-¹
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- A random variable X has the probability density function (pdf) shown in the figure below. fx (*) -2 | 1 3 4 Let us define the events A ={-1s X < 2} and B = {0 < X < 3}. %3D Find c. a) b) Find Fx (x). Find Pr {A} and Pr {B}. Compute Pr {B|A}, the conditional probability of the event A, given B. Compute E[X], E[X\B]. Find k such that Pr{|X| < k} = = f)a) A random variable X has an exponential distribution with probability density function given by f(x) = {ledx; for x 2 0 lo ,elsewhere Find the 75th percentile of X. b) A certain brand of light bulb has a lifespan which is exponentially distribution with a mean of 35 days. 1. What is the probability that a randomly selected light bulb of this brand will last more than 45 days? II. If it is known that a light bulb has already lasted more than 25 days, what is the probability that it will at least last for an additional 50 days. (Hint: Memoryless Property) c) Suppose that the amount of time it takes for someone to finish a task, denoted by X, has the uniform distribution between 20 and 80 minutes. 1. Write a suitable probability density function for the time it takes someone to finish the task. II. Using the density function in (1) above derive the mean of X. II. Derive the variance of X using the results obtained in (I) and (I) above. IV. Find the probability that an individual takes…16. For the probability density function shown, what is the probability of the random variable æ being less than 1/3? f(x)| (A) 0.11 (B) 0.22 (C) 0.25 (D) 0.33 -2 1
- Let X be a continuous random variable whose probability density function is: f(x)- 1.5x2 for -1for clarification since in the picture was cut.. 5. P (X=x) = { 2/9x ² , if ... (refer in the picture)The score of a student on a certain exam is going to be a number between0 and 1. Think of it as the percentage of correct answers on the exam. Suppose the student passes the exam if their score Sis at least 0.60 and fails otherwise. If the probability density function of a student score S is given by 4x f(a) = 4 4xA random variable X has a probability density function given by: Cx +3, -3sxs-2 f(x) ={3-cx, 2sx<3 0, %3D elsewhere 1. Find the value of c that will make the pdf valid. 2. Derive its corresponding distribution function.In 1938, a physicist named Frank Benford discovered that the number 1 appears in the first digit of random data more often than the number 2, the number 2 more often than the number 3 and so on. In general, the probability of occurrence of the first digit of a number can be written in the form of a probability function x + 1 P(X = x) = log. X a. Prove it P(X = x) = log ) untuk x = 1,2,3,4...,9 x+1 X x = 1,2,3,4..., 9 is a probability mass function 2 b. Find the cumulative distribution function of X!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 PAGEBased on their records, a hospital claims that the proportion, p , of full-term babies born weigh over 7 pounds is 40% . A pediatrician who works with several hospitals in the community would like to verify the hopital's claim and investigates. In a random sample of 230 babies born in the community, 111 weighed over 7 pounds. Is there enough evidence to reject the hospital's claim at the 0.05 level of significance? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H0 and the alternative hypothesis H1 . H0: H1: (b) Determine the type of test statistic to use. ▼(Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values. (Round to three or more decimal places.) and (e) Can we reject the claim…52 l l 0.5 If P(A/B)=0.5 and P(B)=0.8, then the 1/1 probability that both A and B occur is O 0.8 O 0.2 O 0.6 0.4 If f(x)=(2x+3)/1O, where 0Suppose that a random variable X has the following probability density function. SC(36-x²) 0 ≤ x ≤ 6 otherwise f(x) = {C (² Find the expected value of X. (You will need to find the value of the constant C so that f is a pdf.)SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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