(Q1): Let P(X=i) be the probability of getting an i when rolling a dice (e.g., i=1, 2, ., 6). What is the value of P(X=i) with the maximum entropy if the following is true? (a) P(X=1) + P(X=2) = ½ (b) P(X=1) + P(X=2) = 1/2 and P(X=6) = 1/3

(Q1): Let P(X=i) be the probability of getting an i when rolling a dice (e.g., i=1, 2, ., 6). What is the value of P(X=i) with the maximum entropy if the following is true? (a) P(X=1) + P(X=2) = ½ (b) P(X=1) + P(X=2) = 1/2 and P(X=6) = 1/3

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: 4. (a) Consider a nonnegative, integer valued random variable Y, and a random sample X1, ·.. , Xn.…

A: Expectation gives the most likely value of a random variable.

Q: The time for the first widget to be manufactured each morning is random between 1 and 3 seconds with…

A: Given density function: fx=1162x-32x+6, 0<x<6 Cumulative distribution function, F(X):…

Q: 1.A machine produces copper wire, and occasionally there is a flaw at some point along the wire. The…

A: Given : f(x) = c(1+x)-3,x>00,x≤0

Q: Let x be the number of teachers among 3 people selected randomly from a group consisting of 3…

A: Probability: Probability is the ratio of favourable outcomes to all other potential outcomes of an…

Q: 1. Let (X) be a simple random walk that starts from X, = 0 and on each step goes up one with…

A: Hello thankyou for the question As per the honor code, we are allowed to answer three parts at a…

Q: The probability of success in a certain game is p. The results in successive trials are independent…

A: Let random variable X be the number of trials performed before r successes are obtained. Then the…

Q: he life X (in years) of a voltage regulator of a car has the pdf f(x) = cx²e (²)³, x>0 a) Find c.…

A: Please note that as per our guidelines if multiple questions are posted we can answer the first…

Q: Suppose that E and F are two events such that Pr[E] = 17/29, Pr[F] = 13/29, and Pr[EN F] = 8/29.…

A: Given, P(E) = 1729P(F) = 1329P(E∩F)=829

Q: Let N(t) be the percentage of a state population infected with a flu virus on week t of an epidemic.…

A: The percentage estimated population would be N(4)=N(3)+N'(3) As(N'(3)=N(4)-N(3)4-3=slope So…

Q: Let X be a discrete random variable taking values {x1, x2, . . . , xn} with probability {p1, p2, . .…

A: Probability Mass Function :- If X is a One-dimensional discrete random variable taking at most a…

Q: Suppose that the conditional distribution of Y given X = x is Poisson with mean E(Y|x) = x, and that…

A: d) From the given information, The conditional distribution of Y given X=x is Poisson distribution…

Q: Experiment X is consist of drawing two balls from a basket containing 13 blue and 5 red balls.…

A: Solution: From the given information, a basket contains 13 blue and 5 red balls. Total number of…

Q: A discrete-valued random variable is defined by its probability mass function P = {p1;P2, . .. Pn},…

A: Probability mass function, P = {p1,p2,...,pn} where, pi are probabilities of outcome Xi So,…

Q: Suppose X has probability generating function GX(t) = 0.2 + 0.3t + 0.1t2 + 0.4t3. What is P(X = 2)?…

A: PGF of a Random Variable is given by, Gx(t) = Σ tx P(X=x)

Q: 1 At the beginning of year 1, Sunco Oil owns i barrels of oil reserves. During year t(t = 1, 2, ...,…

A: According to the given data, first determine the suppositions of the terms mentioned in the problem…

Q: A renewal process has a renewal function M (t) = 4t + (1-e-4t). (a) What is the mean inter-event…

A: Given: Renewal function M(t) = 4t + (1-e-4t)

Q: A particle is confined in a straight tunnel aligned in east-west direction and it can move randomly…

A: Given, The particle moves randomly by the step size of one or two units in east-west direction only.…

Q: 그+ 시X > k) =D P(X> n) 그+서X > k) n) 가+ 시X 2 k) =D P(X > n) 가+ 세x 2 ) > P(X> n)

A: It is an important part of statistics. It is widely used.

Q: Suppose we roll 2 six-sided dice. Let X be their sum and Y be the larger value of the two. (a) (10…

Q: Suppose P(A) = P(B) = 0.2 and P(AN B) = 0.1. What is P(AU B)?

Q: Give an example of a random variable X that takes on values from the set of all binary strings of…

A: @solution::::

Q: •Suppose xau (-54,60) and F(t) is the Cumulative distribution function. which is the probability…

A: Given: Here is the given, X~U-54,60 and the interval -51,-21 and -36,57. To find: The probability…

Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

(Q1): Let P(X=i) be the probability of getting an i
when rolling a dice (e.g., i=1, 2, ..., 6). What is
the value of P(X=i) with the maximum entropy
if the following is true?
(a) P(X=1) + P(X=2) = ½
(b) P(X=1) + P(X=2) = 1/2 and P(X=6) = 1/3
%3D

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Continuous Probability Distribution$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

(d) Experiment: measure the quantities a, b, c (in cm) of rainfall in a day at each of three weather stations A, B and C. Event: it is driest at station A. 2. Suppose we have 2=[0,9]={xR;0
If P(A) = 0.2, P (B) = 0.4 and P(A|B)) = 0.1 Compute P (AUB) Enter your answer with two decimal places.
Suppose X-U (-54, 60) and F(t) is the cumulative distribution function. What is the probability that X is in the interval [-51, -21] or in the interval [-36, 57]? O (F(-21)-F(-51))+ (F(57) - F(-36)) O (F(-21)-F(-51)) x (F(57) - F(-36)) O F(-21)-F(-36) O F(57) - F(-51)
The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of 2 breakdowns every 428 hours. Let x denote the time (in hours) between successive breakdowns. (a) Find λ and Ux. (Write the fraction in reduced form.) ux = f(x) = 214 (b) Write the formula for the exponential probability curve of x. P(x <4) ✔ Answer is complete and correct. 1 P(115
Show that the average time till the first head is observed is y₁= p-¹, where p is the probability of getting a head each time the coin is tossed. Then find a closed form explicit solution to yn, the average time till n consecutive heads are observed for the first time.
g(x) = 3 4+1 if n < x < n + 1 given this function for all nonnegative integers n=0,1,2,3,... and g(x)=0 otherwise. (Hint: I strongly suggest that you graph this function.) 1. Can px(n)=g(n) be the probability mass function of a discrete random variable X that takes values in Z? If not, why, and if so, solve the E[X] and Var(X). 2. Can pY(y)=g(y) be the probability density function of a continuous random variable Y? If not, explain why, and if so, compute E[Y] and Var(Y).