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6. For the probability assignment Pr(x = 1) = (3) ", i=1,2,.. determine: (a) Pr(X <3)...
5. Determine a and Fx(x) for fx(x) given below. Determine Pr(-1 < X < 1) fx(x) 113
be a continuous random variable with probability density function 3. Let for 0 r 1 a, for 2 < < 4 0, elsew here 2 7 fx(x) = (a) Find a to make fx(x) an acceptable probability density function. (b) Determine the (cumulative) distribution function F(x) and draw its graph.
Let X be a random variable with the probability density function f(x)= x^3/4 for an interval 0<x<2 (a) What is the support of X? (b) Letting S be the support of X, pick two numbers a, b e S and compute Pa<x<b). Draw a graph that shows an area under the curve y = f() that is equal to this probability. (c) What is Fx (2)? Draw a good graph of y=Fx (I). (d) What is EX? (e) What is...
Consider fx (x)=e*, 0<x and joint probability density function fx (x, y) = e) for 0<x<y. Determine the following: (a) Conditional probability distribution of Y given X =1. (b) ECY X = 1) = (c) P(Y <2 X = 1) = (d) Conditional probability distribution of X given Y = 4.
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
- ACUJU 1. (6%) Let X be a random variable with probability distribution (1+x **,-1<x< 1 0, elsewhere Find the probability distribution of the random variable Y = X2.
6. Define a Markov Chain on S- 10, 1,2, 3,...) with transition probabilities Po,1 1, with 0<p<1 (a) Is the MC irreducible? (b) For which values of p the Markov Chain is reversible?
Find Pr[2 5B(15,.1) <3] . That is, if X is a binomial random variable counting successes on n=15 Bernoulli trials with p=.1, find the probability that x is between 2 and 3, inclusive. O A.0.3954 O B. 0.1286 O c.1.7604 O d. 0.4383 O E.0.1714
1 pt) A P(X1126) Probability B. P(X < 966) Probability c. P(X > 1046) Probability
[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]