2. Suppose the cumulative distribution function of the random variable X is x < -2, - 2 < x < 2, 2< x. F(x) = 0.25x + 0.5 1
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a) Determine the probability density
b) Find P(x>-1.5)
c) Find p(x<1.8)
![2. Suppose the cumulative distribution function of the random variable X is
x < -2,
- 2 < x < 2,
2< x.
F(x) =
0.25x + 0.5
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- The probability density function (p.d.f.) of a continuous random variable X is defined to be: kx + for 0 < x < 1 f(x) = |0 otherwise, for some constant k. For these problems, please ensure your answers are accurate to within 3 decimals. Part a) Find the value of k that makes the above function a proper p.d.f. Part b) Find E(X).4X and Y are independent, X ~ U (0, 1) and Y U (0, 1). Calculate the probability P(X+Y<1.5).
- 1.The probability density function of a continuous random variable X is given by f(x) : 04 i) Find k ii) Find P (1.5(c) At a bus stop, there are two buses available (bus numbers 1 and 2). For i = 1,2, the waiting time until bus i arrives is denoted by T;, with T independent of T2, and T; has density function fr. (t) = X, exp(-1;t), t>0.Suppose a random variable X has a probability density function given by O elsewhere f (x) = kx (1 − x) 0 ≤ x ≤ 1 0 elsewhere a. Find the value of k that makes this a probability density function b. Find P (0.4 ≤ x ≤ 1) c. Find P(x ≤ 0.4) d. Find P (0.8 ≤ x))Suppose that X is a continuous random variable with a probability density function is given by f(x)= 25 when x is between -2 and 2, and f(x)=0 otherwise. a.)Find E(X2), where X is raised to the power 2 b.) Find Var(2X+2)If X has the probability density * 21 f(2): 2 <1 Find P (1 < X < 5). Select one: O a. 0.93 O b. 0.96 O G 0.12 O d. 0.91A continuous random variable X has density function f(x) = 1.5(1 – x²), 0 < x < 1. a) Calculate the expected value of X. b) Calculate the expected value of X?. c) Calculate the standard deviation of X. d) Calculate the expected value of Y = 4X + 5. e) Calculate the standard deviation of Y = 4X + 5.for a population with a standard deviation of 4.2 and mean of 32.5, draw a bell shaped curve, marking location of the mean and the numbers that correspond with all the standard deviations Type your answer here:|A 9 a) The continuous random variable Xhas probability density function f (x) = 0(1– x)"-1 , 0 0 i) Find the cumulative distribution function, F(x), of X ii) Find P(0.25Find c to get a probability mass function.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