![1) [15 pts.] Let Z be a discrete random variable having possible values 0, 1,2, and 3 and probability mass function p(0)-1/4,](http://img.homeworklib.com/questions/8c9f0420-c72b-11eb-9ccf-993e17c4fac8.png?x-oss-process=image/resize,w_560)
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![CU c) To detegimine the voliance voy+) we know that RV(Z) = f(++)-Cec7)]- we know that E): 1125 [E (7)] = (1.125) = 1.265. [](http://img.homeworklib.com/questions/8ed34920-c72b-11eb-b9c0-99efd79e2215.png?x-oss-process=image/resize,w_560)
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1) [15 pts.] Let Z be a discrete random variable having possible values 0, 1,2, and...
5. Let X be a discrete random variable. The following table shows its possible values associated...
5. Let X be a discrete random variable. The following table shows its possible values associated probabilities P(X)( and the f(x) 2/8 3/8 2/8 1/8 (a) Verify that f(x) is a probability mass function. (b) Calculate P(X < 1), P(X 1), and P(X < 0.5 or X >2) (c) Find the cumulative distribution function of X. (d) Compute the mean and the variance of X.
5. Let X be a discrete random variable. The following table shows its possible values r...
5. Let X be a discrete random variable. The following table shows its possible values r and the associated probabilities P(X -f(x) 013 (a) Verify that f(x) is a probability mass function (b) Calculate P(X < 1), P(X < 1), and P(X < 0.5 or X > 2). (c) Find the cumulative distribution function of X ompute the mean and the variance of
using excel answer the problem below Let X be a discrete random variable having following probability...
using excel answer the problem below
Let X be a discrete random variable having following probability distribution. x 2 4 6 8 P(x) 0.2 0.35 0.3 0.15 Complete the following table and compute mean and variance for X x P(x) x· P(x) x2. P(x) 2 0.2 4 0.35 6 0.3 8 0.15 Total 1 Expected value E(X) = u = Variance Var = o2 =
Problem 3 A discrete random variable Y takes values {k= 0, 1, 2, ...,} such that...
Problem 3 A discrete random variable Y takes values {k= 0, 1, 2, ...,} such that PLY Z k} = ()* for k 20. 1. Derive P[Y = k) for any k > 0. 2. Evaluate expectation, E[Y] = 3. Given E[Y(Y - 1)] = 15 , find variance of Y, Var[Y] =
4.8. Let Z be a random variable with the geometric probability mass function where 0 <...
4.8. Let Z be a random variable with the geometric probability mass function where 0 < π < 1. (a) Show that Z has a constant failure rate in the sense that PriZ kZk1 T for k 0, 1,.... (b) Suppose Z' is a discrete random variable whose possible values are 0, 1, and for which Pr(Z'=KZ2k} = 1-π for k 0,1,.... Show that the probability mass function for Z' is p(k).
2. Let X be a discrete random variable with the following cumulative distribution function 0 0.2...
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.
please show you steps, and add some exppanation if possible. Thank you! 5. Let X associated...
please show you steps, and add some exppanation if
possible. Thank you!
5. Let X associated probabilities P(X = x)-/(2) be a discrete random variable. The following table shows its possible values r and the () 2/8 3/8 2/8 1/8 (a) Verify that f(x) is a probability mass function. (b) Calculate P(X < 1), P(X s 1), and P(X0.5 or Xx> 2) (c) Find the cumulative distribution function of X. (d) Compute the mean and the variance of X
2. For a discrete random variable X, with CDF F(X), it is possible to show that...
2. For a discrete random variable X, with CDF F(X), it is possible to show that P(a < X S b)-F(b) - F(a), for a 3 b. This is a useful fact for finding the probabil- ity that a random variable falls within a certain range. In particular, let X be a random variable with pmf p( 2 tor c-1,2 a. Find the CDF of X b. Find P(X X 5). c. Find P(X> 4). 3. Let X be a...
Let p(z)=1/5 be the probability distribution function for random variable X with z=5, 10, 15, 20,...
Let p(z)=1/5 be the probability distribution function for random variable X with z=5, 10, 15, 20, 25. Find the mean and variance of Z..
1. Consider a discrete random variable, X, where the outcome of this random variable is determined...
1. Consider a discrete random variable, X, where the outcome of this random variable is determined by throwing a 6-sided die. X takes on integer values 1,2,…,6. The die is fair. That is, P(X=1)= P(X=2)=…= P(X=6). i. Draw the probability distribution function for this random variable. Carefully label the graph. ii. Draw the cumulative distribution function for X. iii. Calculate the following: P(X=4) P(X≠5) P(X=1 or X=6) P(X4) E(X) Var(X) sd(X) iv. Consider the random variable Y where the outcome...
5. Let X be a discrete random variable. The following table shows its possible values associated probabilities P(X)( and the f(x) 2/8 3/8 2/8 1/8 (a) Verify that f(x) is a probability mass function. (b) Calculate P(X < 1), P(X 1), and P(X < 0.5 or X >2) (c) Find the cumulative distribution function of X. (d) Compute the mean and the variance of X.
5. Let X be a discrete random variable. The following table shows its possible values r and the associated probabilities P(X -f(x) 013 (a) Verify that f(x) is a probability mass function (b) Calculate P(X < 1), P(X < 1), and P(X < 0.5 or X > 2). (c) Find the cumulative distribution function of X ompute the mean and the variance of
using excel answer the problem below
Let X be a discrete random variable having following probability distribution. x 2 4 6 8 P(x) 0.2 0.35 0.3 0.15 Complete the following table and compute mean and variance for X x P(x) x· P(x) x2. P(x) 2 0.2 4 0.35 6 0.3 8 0.15 Total 1 Expected value E(X) = u = Variance Var = o2 =
Problem 3 A discrete random variable Y takes values {k= 0, 1, 2, ...,} such that PLY Z k} = ()* for k 20. 1. Derive P[Y = k) for any k > 0. 2. Evaluate expectation, E[Y] = 3. Given E[Y(Y - 1)] = 15 , find variance of Y, Var[Y] =
4.8. Let Z be a random variable with the geometric probability mass function where 0 < π < 1. (a) Show that Z has a constant failure rate in the sense that PriZ kZk1 T for k 0, 1,.... (b) Suppose Z' is a discrete random variable whose possible values are 0, 1, and for which Pr(Z'=KZ2k} = 1-π for k 0,1,.... Show that the probability mass function for Z' is p(k).
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.
please show you steps, and add some exppanation if
possible. Thank you!
5. Let X associated probabilities P(X = x)-/(2) be a discrete random variable. The following table shows its possible values r and the () 2/8 3/8 2/8 1/8 (a) Verify that f(x) is a probability mass function. (b) Calculate P(X < 1), P(X s 1), and P(X0.5 or Xx> 2) (c) Find the cumulative distribution function of X. (d) Compute the mean and the variance of X
2. For a discrete random variable X, with CDF F(X), it is possible to show that P(a < X S b)-F(b) - F(a), for a 3 b. This is a useful fact for finding the probabil- ity that a random variable falls within a certain range. In particular, let X be a random variable with pmf p( 2 tor c-1,2 a. Find the CDF of X b. Find P(X X 5). c. Find P(X> 4). 3. Let X be a...
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