For each of the following functions, (i) find the constant c so that f(x) is a...
(b) Let X be a continuous random variable with pdf given by: f(x) =c#x Find the constant c so that f(x) is a pdf of a random variable. C (ii) Find the distribution function F(x)P(X Sx)X (ii) Find the mean and variance of X. .Col니loa, ,iaaa4
BSP2014 5. Given xe 20 Cr) 0 x<0 i) Show thatAx) is a pdf. ii) Find the cumulative distribution function (CDF) of X 6. The p.d.fof a random variable Y is given by y +1 for2<y<4 v) 0 elsewhere Find i) the value of c ii) P(Y<3.2) iii)P(2.9 < γ< 3.2) 7. The p.d.fof a random variable X is given by elsewhere i) Find P(X<1.5) ii) Find P(0.5 X1.5)
1. Let X~b(x; n, p) (a) For n 6, p .2, find () Prx> 3), (ii) Pr(x23), (ii) Pr(x (b) For n = 15, p= .8, find (i) Pr(X-2), (ii) Pr(X-12), (iii) Pr(X-8). (c) For n 10, find p so that Pr(X 2 8)6778. く2). 2. Let X be a binomial random variable with μ-6 and σ2-2.4. Fin (a) Pr(X> 2) (b) Pr(2 < X < 8). (c) Pr(Xs 8). 1. Let X~b(x; n, p) (a) For n 6, p...
Please answer me clearly so I can read well BSP2014 Tutorial 2 1. Check whether the given function can serve as the probability mass function(p.m.f.) of a random variable 2forx-1,2, 3,4, 5 ii) Ax)for-0,1,2, 3,4 2. A random variable X has the following probability distribution. 0.1 2k 0.3 i)Find k ii)Evaluate PX2 and P-2X2) iii) Find the CDF of X 3. If X has the cumulative distribution function, CDF Fix) = I/2 , 1 xc3 x25 Find a) PXS 3)...
The probability density function of a continuous random variable X is given as shown. I f(x) a) (7.5 pts) Find the value of the constant k as a fraction. b) (7.5 pts) Find the probability P(1sx53). c) (5 pts) Find the value of x such that P(Xsx)=0.5.
X follows normal distribution N (μ, σ2) with pdf f and cdf F. If max, f (x)-0.997356 and F (-1) + F (7-1, determine P(X s 0)
Question 1. Consider these real-valued functions of two variables f(x, y) (a) (i) What is the maximal domain, D, for the functions f and g? Write D in set notation (ii) What is the range of f and g? Is either function onto? (iii) Show that f is not one-to-one. (iv) Find and sketch the level sets of g with heights: 20-0, 20-2, 20-4 (Note: Use set notation, and draw a single contour diagram.) (v) Without finding Vg, on your...
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
A discrete random variable X has the following probability distribution: x7778798081 P(x) 0.150.150.200.400.10Compute each of the following quantities. i. P(X = 80) ii. P(x > 80) iii. P(X ≤ 80) iv. The mean, μ of x. v. The variance, σ2 of X. vi. The standard deviation, σ of X.
Question 1 A continuous random variable X which represents the amount of sugar (in kg) used by a family per week, has the probability density function c(x-1(2-xsxs2 ; otherwise f(x) (i) Determine the value of c ii) Obtain cumulative distribution function (iii) Find P(X<1.2). Question 2 Consider the following cumulative distribution function for X 0.3 0.6 0.8 0.9 1.0 (i) Determine the probability distribution. ii) Find P(X<1). iii Find P(O <Xs5). Consider the following pdf ,f(x) = 2k ; 1<x<2...