Consider the following random variable based on throwing a dice -2 for 0 for Norg or...
A random experiment consists of throwing two three-sided dice (show- ing the numbers 1, 2, 3). Let Y be the random variable which records the product of the pair of numbers showing on the dice. (i) Write down the range RY of Y . (ii) Determine the probability distribution of Y . (iii) Calculate E(Y ) and V (Y ).
Part I - Throwing a Dice with Six Faces (32 points) Consider a dice with six faces, i.e. a standard dice. The possible outcomes after throwing the dice once are 1, 2,3, 4,5,6 (a) Assume that the dice is thrown once. Let w represents the outcome. Explain why P(w-i) for i = i..6, when the dice is fair (b) The fair dice is thrown twice. Find the probability of occurance of at least one 6 The fair dice is thrown...
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...
The random variable Q is uniform on [0,1] . Conditioned on Q=q , the random variable X is Bernoulli with parameter q . A uniform random variable on [0,1] has a variance of 1/12 and also satisfies E[Q2]=1/3 . Then: Var(E[X|Q])= ? E[Var(X|Q)]= ?
In an experiment with throwing 2 fair dice, consider the events A : The sum of numbers on the faces is 8 B : Doubles are thrown. What is the probability of getting A or B ?
Consider the following PDF for a continus random variable f(x) X: 0 x<0,4 Calculate K Calculate P0, 1<x<0,3) Calculate P(X <= 0,2) Calculate E(X) Calculate Var(X) 3,75-Kx®2]
Consider a random variable X with the following properties E[X] = 20 and var(X) = 2. Consider a new random variable such that Y = 5 – 5X Calculate the following. (a) E[Y] = = (b) var(Y) = À
Consider three six-sided dice, and let random variable Y = the value of the face for each. The probability mass of function of Y is given by the following table: y 1 2 3 4 5 6 otherwise P(Y=y) 0.35 0.30 0.25 0.05 0.03 0.02 0 Roll the three dice and let random variable X = sum of the three faces. Repeat this experiment 50000 times. Find the simulated probability mass function (pmf) of random variable X. Find the simulated...
Consider a random variable X with the following properties E[X] - 10 and var(X) - 9. Consider a new random variable such that Y-1-5X Calculate the following (a) EY] - (b) var(Y) = 5
B. Consider an experiment where two dice are rolled. Define the random variable X as the absolute difference between the face-up values on the two dice. i. Determine the probability that Xis 0. ii. Determine the probability that Xis not 4 iii. Sketch the probability mass function for X.