4. A mixed random variable X has the cumulative distribution function: (0. for x < 0.4...
A mixed random variable X has the cumulative distribution function e+1 (a) Find the probability density function. (b) Find P(0< X < 1).
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]
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):
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.
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0 if x < 0 0.2 if 0 < x < 1 Ex(x) = {0.5 if 1 < x < 2 0.9 if 2 < x <3 11 if x > 3 a)Give the probability mass function of X, explicitly. b) Compute P(2 < X < 3). c) Compute P(x > 2). d) Compute P(X21|XS 2).
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.
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...
[Total Marks: 301 ={} Question 1 A random variable X has a probability density function as defined below. (x + 1 -1<x<0 fx(x) = (-x+1 0<x< 1 Find the following: a) The cumulative distribution function of X, Fx(x). b) P(x > 0.1 X < 0.5). c) The conditional probability density function fx(x = 0.6 X > 0.5). [10 Marks [5 Marks [15 Marks]
6. The distribution law of random variable X is given -0.4 -0.2 0 0.1 0.4 0.3 0.2 0.6 Xi Pi Find the variance of random variable X. 7. Let X be a continuous random variable whose probability density function is: f(x)=Ice + ax, ifXE (0,1) if x ¢ (0:1) 0, Find 1) the coefficient a; 2) P(O.5 X<0.7); 3) P(X>3). Part 3. Statistics A sample of measurements is given Y 8 4 2 2 0 8. Compute the coefficient of...
4.3.2 The cumulative distribution func- tion of random variable X is 0 r<-1, Fx (x) = (z + 1)2-1 x < 1, r1 Find the PDF fx(a) of X