If X has the distribution function F(x) = 0 for x < 1 0.20 for 1 12 (a) Determine the probability distribution function of X using the limit formula. (b) P(X = 3) (c) P(X ≥ 1)
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- f(x) x2 for -1 sx < 1, and O for any other value of x %3D 1 then, the percentage probability P is4. The cumulative distribution function of a continuous random variable, X is given as follows: x<0 F(x) = - x(x+4), 32 0Sx<4 1 x24 (a) Calculate P(|X-1|<1). (b) Find the median. (c) Determine the probability density function of X. Hence, evaluate E(3X² -1).Using 2 independent DRVS X and Y with probability distribution px(x) and py (y) below, find E(Z) where Z = X + Y X 1 2 3 4 Px(x) 1/8 3/16 3/8 3/16 1/8 Y 3 4 5 Py(y) 1/4 1/4 1/4 1/4
- 1. Let X be the mean of a random sample of size n = 64 from the exponential distribution e-2/², x>0 otherwise 0, f(x)= = Based on central limit theorem, approximate the probability P (1.8 < X < 2.1). Round your final answer to 4 decimals.1. Let X have the probability density function f(x) = cx(1-2) for 0≤x≤ 1 and f(x) = 0 otherwise. (a) Show that c = 6. (b) Find the cumulative distribution function F(x) = P(X ≤ z). (c) Calculate P(.1 < X <5). (d) Find the mean, variance and standard deviation of X.3. A random variable X has a cumulative distribution function if 0 0.5). (e) Find P(X < 1.25). (f) Find P(X = 1.25).
- Denote by a* 0 < x <1 0.5 2 <*f(x) 0.15 0.19 [Q3] The continuous joint probability distribution is expressed below. Find: c, and P(X <3, Y < 4). (Work at precision of 4 digits after the decimal point.) for 2 < x < 4, 3 < y < 5 f(x, y): [cy²e- lo elsewhere2. A random variable X has a p.d.f. f(x) given by √(1-x)6 0Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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