Suppose x is a random variable best described by a uniform probability that ranges from 0 to 5. Compute the following: (a) the probability density function f(x) = (b) the mean µ = (c) the standard deviation o = (d) P(µ – o < x 2.41) =
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- Suppose a random variable has a continuous uniform distribution between 0 and 10, such that its probability density function is: f(x) = 1/10. a. What is the cumulative density function for x? b. What is the mean (expected value) of x? c. What is the variance of x? d. According to Chebychef's rule, what is the smallest probability a random x will within 2 standard deviations of its mean? i.e. P(x-μ<2*o) e. What is the exact probability that a random x will fall within 2 standard deviations of its mean for this uniform distribution?Q.7 For an exponential distribution fx(x; 4) = (ue Hx: x 20 %3D where u > 0 Write (Don't derive) (a) Mean (expected value), i.e. E(X). (b) Standard deviation, i.e. S.D. (X). (c) Moment generating function, i.e. Mx(t). (d) Cumulative distribution function (cdf), Fx(x). of Nizwx is a gaussian random variable with a PDF as described above, where μ is the mean, σ is the standard deviation , and Fx(X) refers to the cumulative distribution function CDF. It is known that Fx(-0.7) = 0.500 and Fx(1.3)=0.841, what value of Xo do we find the probability Fx(Xo) = P(X<Xo) = 0.023 ?
- A random variable X has the following pdf: f (x) = 9xe-3";x > 0 %3D (a) Calculate the expected value of the distribution, E(X). (b) Calculate the mode of the distribution (no need to show the second derivative).Consider the continuous random variable with probability density function fx(x) = 3x² for 03) Suppose X is a discrete variable that has the following pr function (pdf) f (X) 1. 0.40 0.20 3 0.15 4. 0.25 a) Calculate the cumulative distribution function (the b) Find the expected value, showing your work: E(X) c) Find the variance, showing your work: Var (X)2. where The random variable, X, has a probability density function (pdf), f(x), and zero otherwise. (a.) (b) x+1, f(x) = {1x, 1 81 -1/2 < x < 0 0(a), (b), (c)the probability density function for the waiting time was given by f(x) = 0 for x 15 a) Find the expected value of the waiting time, X minutes. b) Find the variance and standard deviation of the waiting time. c) What is the probability that the waiting time is within two standard devia- tions of its expected mean value? 1 15Recommended 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