Let X be the outcome of rolling a fair six-sided dice. The possible outcomes or X...

Let X be the outcome of rolling a fair six-sided dice. The possible outcomes or X are 1,2,3,4,5 and 6 and all are equally likely. What is the cumulative distribution function F(x)?

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orchestra answered 2 years ago

Let a random experiment consist of tossing two fair six sided dice. Let x be the...

Let a random experiment consist of tossing two fair six sided dice. Let x be the minimum number shown on the dice. Determine the closed form PMF of x. Hint: Creating a chart for all possible combinations of the two rolls may be helpful.

Consider the experiment of rolling a six-sided fair die. Let X denote the number of rolls...

Consider the experiment of rolling a six-sided fair die. Let X denote the number of rolls it takes to obtain the first 5, Y denote the number of rolls until the first 2, and Z denote the number of rolls until the first 4. Numerical answers are needed only for parts (a) and (b). Expressions are sufficient for parts (c), (d), and (e). a) E[X|Y = 1 or Z = 1] b) E[X|Y = 1 and Z = 2] c)...

An experiment consists of rolling six-sided dice twice. &

An experiment consists of rolling six-sided dice twice. (10) List the sample space for this experiment. Find the probability distribution for this experiment where x represents the number of even numbers in the 2 rolls. Find the mean of the probability distribution. Find the standard deviation of the probability distribution. Would it be unusual to get 2 even numbers? Why or why not? (show your work)

1. Three six-sided dice are rolled. Let X be the sum of the dice. Determine the...

1. Three six-sided dice are rolled. Let X be the sum of the dice. Determine the range of X and compute P(X = 18) and P(X ≤ 4). 2. An urn contains 5 red balls and 3 green balls. (a) Draw 3 balls with replacement. Let X be the number of red balls drawn. Determine the range of X and compute P(X = 3) and P(X 6= 1). (b) Draw 3 balls without replacement. Let Y be the number of...

When two fair six-sided dice are simultaneously thrown, these are two of the possible results that...

When two fair six-sided dice are simultaneously thrown, these are two of the possible results that could occur: Result 1: a 5 and a 6 are obtained in any order. result 2: a 5 is obtained on each die. Which of the following statements is correct? Explain reasoning. a. the prob. is equal b. prob of result 1 is higher c. prob of result 2 is higher

A fair 4-sided die is rolled, let X denote the outcome. After that, if X =...

A fair 4-sided die is rolled, let X denote the outcome. After that, if X = x, then x fair coins are tossed, let Y denote the number of Tails observed. a) Find P( X >= 3 | Y = 0 ). b) Find E( X | Y = 2 ). “Hint”: Construct the joint probability distribution for ( X, Y ) first. Write it in the form of a rectangular array with x = 1, 2, 3, 4 and...

7. [10 marks] Consider an experiment of rolling two regular (or fair) balanced six-sided dice. a)...

7. [10 marks] Consider an experiment of rolling two regular (or fair) balanced six-sided dice. a) List out all the possible outcomes. b) Define X as the amount you will win in the following game. You will win $100 when a double (two identical numbers) is rolled; you will win $10 when an odd sum is rolled; and you will win $30 when other even sum is rolled, excluding doubles. Define X as the amount you will win in this...

Suppose you are rolling a fair four-sided die and a fair six-sided die and you are...

Suppose you are rolling a fair four-sided die and a fair six-sided die and you are counting the number of ones that come up. a) Distinguish between the outcomes and events. b) What is the probability that both die roll ones? c) What is the probability that exactly one die rolls a one? d) What is the probability that neither die rolls a one? e) What is the expected number of ones? f) If you did this 1000 times, approximately...

Two fair dice are rolled and the outcomes are recorded. Let X denotes the larger of...

Two fair dice are rolled and the outcomes are recorded. Let X denotes the larger of the two numbers obtained and Y the smaller of the two numbers obtained. Determine probability mass functions for X and Y, and the cumulative distribution functions for X and for Y. Present the two cumulative distribution functions in a plot. Calculate E (2X + 2Y −8).

Assume a fair six-sided dice is rolled r times. Let Y be the random variable for...

Assume a fair six-sided dice is rolled r times. Let Y be the random variable for the number of faces that appeared exactly twice. Find E[Y].

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