A random variable 'X' has the following cumulative distribution function:
0 if x < 1
0.25 if 1 <= x < 2
F(x) = 0.4 if 2 <= x < 4
0.7 if 4 <= x < 6
1 if x >= 6
Give the mass function of X:
what is Var(X):
A random variable 'X' has the following cumulative distribution function: 0 if x < 1 0.25...
4. A mixed random variable X has the cumulative distribution function: (0. for x < 0.4 X2 – 0.02 for 0.4 < x < 0.5 Fx(xx) = { 0.2.x3 + 0.6x + 0.25 for 0.5 < x < 0.7 for x > 0.7 (a) Calculate the mean and standard deviation of X. (b) Find P(0.44 < X < 0.62).
Random variable X has the following cumulative distribution function: 0 x〈1 0.12 1Sx <2 F(x) 0.40 2 x<5 0.79 5 x<9 1x29 a. Find the probability mass function of X. b. Find E[X] c. Find E[1/(2X+3)] d. Find Var[X]
3. The cumulative distribution function of a random variable Y is: 0 if y<-1, 0.3 if -1 y <0.5, 0.7 Fr (y)- y < 2, if 0.5 1 if y 2 2. (a) Draw a sketch plot of Fy (y) d) Find the probability mass function, fz(2), of Z -Y2 (e Find El2] and Var(Z) (f) Find El2-321 and Var(2-32). 13 marks]
Problem 6. Consider a random variable X whose cumulative distribution function (cdf) is given by 0 0.1 0.4 0.5 0.5 + q if -2 f 0 r< 2.2 if 2.2<a<3 If 3 < x < 4 We are also told that P(X > 3) = 0.1. (a) What is q? (b) Compute P(X2 -2> 2) (c) What is p(0)? What is p(1)? What is p(P(X S0)? (Here, p(.) denotes the probability mass function (pmf) for X) (d) Sketch a plot...
2. Let X be a discrete random variable with the following cumulative distribution function 0 0.2 0.5 ェ<2, 2-1<5.7, 5.7-1 6.5, 6.5 <エ<8.5, F(z)= 18.5 エ a) Find the probability mass function of X b) Find the probabilities P(x>5), P(4<X 6x> 5) c) If E(X) = 5.76, find c.
Question 2 If the random variable X has the following cumulative distribution function, find the cumulative distribution function for Z vX. x < -1, x< 0, Fx(x) 1/3, 1,
(6 points) The continuous random variable X has cumulative distribution function given by 0 for x <0 for x > 2 Part(a) Find the value of c correct to one decimal place given that E(X c) 4E(X - c). 0.4 Part(b) Two independent observations of X are taken. Find the probability correct to 2 decimal places that one is less than 1 and the other is greater than 1. The order in which we take the observations matters. Part(c) Find...
Show steps, thanks! 2.5.9. The random variable X has a cumulative distribution function 0, forx<0 F(x) for x > 0. for x > , 1+x2" · Find the probability density function of X.
(6 points) The continuous random variable X has cumulative distribution function given by 0 for0 for 0 < z < 2 for 2 F(z) = 〈 z-4z2 Part(a) Find Var(X), correct to 2 decimal places. Part(b) Find E(X) correct to 2 decimal places. Part(c) Find P(X>) Give your answer as a decimal, correct to 2 decimal places. Part(d) Find E(X), correct to 2 decimal places. Part(e) Find the value of c correct to one decimal place given that E(Xc) 4E(X-c...
1. A random variable X has the cumulative distribution function exe F(X) = 1 + ex • Find the probability density function • Find P(0 < X < 1)