Question 2 (total 20 marks) When a fair coin is tossed, 10 points are scored if a head is obtained and 20 points arescored if a tail is obtained. Suppose that the coin is tossedtwo times and let the random variable X be the total score obtained.(a) What is the state space of X?(b) What is the probability mass function of X? Draw the line graph of the probability mass function.(c) What is the cumulative distribution function of X? Draw the graph of the cumulativedistribution function.(d) What is the expectation of X?(e) What is the standard deviation of X?

2(a).Step 1: Given data ;When a fair coin is tossed, 10 points are scored if a head is obtained and…

Answered: Question 2 (total 20 marks) When a fair…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Dppp5
Coin A has a probability of head equal to 1/4 and probability of tail equal to 3/4 and coin B is a fair coin. Each coin is flipped four times. Let the random variable X denote the number of heads resulting from coin A and Y denote the resulting number of heads from coin B. (a) What is the probability that X = Y = 2 ? (b) What is the probability that X = Y ? (c) What is the probability that X > Y? (d) What is the probability that X + Y< 5?
12.THEORY OF DISTRIBUTIONS
Q2\ Calculate the cumulative distribution function (CDF) for the probability mass function: Events probability 0.11 B 0.2 0.32 0.05 0.32
Correction: 1b) What is E?
Question* Let Xbe a random vanable with probability distribution as shown below: S(1)-3 ekewhere Then the value of /g(X)s O Nore of these
Question * Let X be a random variable with probability distribution as shown below: -1sxs2 S(x)=. and g(X)=4X +2 elsewhere Then the value of E(g(X)) is: 10 8 7 None of these
Random variable X has the binomial distribution with n=100 and p=0.25. By using binomial probability table, find a)p(x<20) b)p(x<=15) c)p(20<x<30)
probability
(a) Sketch the probability mass function of X . (b) Find the mean and standard deviation of the number of pots of olives sold daily. (c) If the profit obtained from selling a pot of olives is 50p, what is the expected profit made on a single day? During a working week of 6 days?
part (i), (ii) and (iii) is already answered. could you answer part (iv) only i. Two six-sided dice are rolled and the scores added together. Draw the sample space, the probability density function and the cumulative probability density function by hand. ii. What is the probability that the number obtained on one of the dice is a multiple of a number obtained on the other dice? What is the probability of doubles (1,1, 2,2. etc)? iii. A weekly lottery with numbers 1-49 has come up with the numbers 2,4,6,8,10 and 20,25,30,35,40 over the last month. There have been claims of fraud and the organisers are worried as ticket sales are down.Write a short paragraph on the issue giving views based on yourknowledge of probability. iv. Use six letter word to explain and illustrate the differences between permutations and combinations. Give an example where the distinction between permutations and combinations is crucial.
Depending on the input a computer program takes variable number of cycles to come up with the answer. Let X be the random variable which takes on the values k = 1,2,3,··· ,infinity for the number of cycles required to come up with the answer where 1 is the possibility that the program never arrives at an answer. (a) The probability mass function (p.m.f) for completing in k cycles is p_X(k) = (2^k)/(3^(k+1)) , k = 1,2,3,··· . What is the probability that the computer program never completes? (b) Use part (a) to find probability P (X greater or equal 3). Write your answer in a simplest fraction. (c) Given that the program has not found the answer after 2 cycles, what is the probability that it will never find the answer?

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