The random variable X takes the values -2, -1 and 3 according to the following probability...
The following table shows the probability distribution of a random variable X 2 -2 -1 0 1 х с f(x) 2k k 3k 0.3 0.1 It is given that E(5X 2) 3; (a) Find c and k; (4
Question 2 a) A random variable X has the probability function f(x) = k·(7 - x) for x = 1,2,...,6 Write down the probability distribution of X i. (3 marks) (3 marks) ii. Show that k = 1/21 Find E(X) and Var(X) Deduce the standard deviation, dy from Var(X). (3 + 3 marks) (1 mark) iv
2) Consider a random variable with the following probability distribution: P(X-0)-0., Px-1)-0.2, PX-2)-0.3, PX-3) -0.3, and PX-4)-0.1 A. Generate 400 values of this random variable with the given probability distribution using simulation. B. Compare the distribution of simulated values to the given probability distribution. Is the simulated distribution indicative of the given probability distribution? Explain why or why not. C. Compute the mean and standard deviation of the distribution of simulated values. How do these summary measures compare to the...
The Bernoulli random variable takes values 0 and 1, and has probability function f(x) = px (1 − p)1−x(a) By calculating f(0) and f(1), give a practical example of a Bernoulli experiment, and a Bernoulli random variable. (b) Calculate the mean and variance of the Bernoulli random variable.
6. (Entropy) The Bernoulli random variable X takes on the values 0, 1 with equal probability, i.e. PX pX Compute El(x) if where logs are to base 2
X = o,1,2,3 and P(X)= 2k,3k,13k,2k. how is this problem done? a random variable X has a probability distribution as follows done? What is K and why is its value .05 Total probability = 1 2k+3k+13k+2k= 1 k= .05 p(x<2)= 2k + 3k = 5k = 5*.05=.25 Answer is B 0.25
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] =
3 (17') The random variable X obeys the distribution Binomial(n,p) with n=3, p=0.4. (a) Write Px(x), the PMF of X. Be sure to write the value of Px(x) for all x from - to too. (b) Sketch the graph of the PMF Px [2] (c) Find E[X], the expected value of X. (d) Find Var[X], the variance of X.
The discrete random variable X has the following probability mass function: f(x) = kx, for the values of x = 2,4,5 and 6 only. Find the i. value of k. ii. construct the probability distribution of X iii. expected value and standard deviation X
sc I The discrete random variable X has the following probability mass function: P(X = x) = kx for the values of x = 2,4 and 5 only. Find the i. value of k. expected value and the variance of X. iii. cumulative distribution function of X, F(x).