Answer :
given data :-
The experiment of rolling a die once
the out comes are = {i:i E [1,6] ,Let X = ln(i),
where,
iE [1,6]. Is X a random variable
let,
truly x is random variable in light of the fact that the estimation of x is same to the individual estimations of i and since i is an arbitrary variable as changed its likelihood space to x
x is a random variable
In the experiment of rolling a die once, the outcomes are {i: 1 E [1,6]. Let...
1. An experiment consists of rolling a die once. The experiment is interested in the event: an even numbered face comes up. (a) How would you define a random variable so that it would be Bernoulli? (b) Is it necessary for the die to be fair? Explain. (c) If the die is fair, what is p? (d) If the die is biased such that an even face is three times as likely to come up as an odd face, what...
Let us consider the experiment of rolling a die twice and define Ω = {(1, 1), · · · ,(6, 6)} which contains all 36 possible outcomes. Assume that all outcomes are equally likely: P({ω}) = P({(i, j)}) = 1/36 for all i, j = 1, 2, · · · 6. Thus, (1, 2) ∈ Ω corresponds to the first outcome being 1 and the second outcome being 2. Define X = i, if the first outcome is i, i...
Back to the experiment of rolling the fair octahedral die. Let Y=1 if you get a 7, or 0 otherwise. What kind of a random variable is Y? A Bin(8; 1/6) B Bern(1/7) C Bern(1/8) How many different values takes the pmf of Y? A 1 B 2 C 8
Problem 5. (8 points) Consider rolling a six-sided die. Let A be the set of outcomes where the roll is an even number Let B be the set of outcomes where the roll is greater than 3. Calculate the sets on both sides of De Morgan's laws and verify that the equality holds. (AUB)c A n B
1. Consider the experiment: You flip a coin once and roll a six-sided die once. Let A be the event that you roll an even number and B be the event that you flip heads. (a) Determine the sample space S for this experiment. (Hint: There are 12 elements of the sample space.) (b) Which outcomes are in A? (c) Which outcomes are in B? (d) Which outcomes are in A'? What does it mean in words? (e) Which outcomes...
7. Suppose that an experiment has two outcomes 0 or 1 (such as flipping a coin). Suppose that independent experiments and for the ith experiment you let the random variable X Ber(p) with we will assume for this problem that p is the same for each i). Then, you run n tell you the outcome for 1 isn. Then we can assume that for each i, that X p P(X 1) (where ΣΧ. let X (a) What is the state...
Let X1 be a random variable whose value is the result of rolling an 8- sided die, and X2 a random variable whose value is the result of rolling a 12-sided die. (1) Find E(X1 + X2). (2) Find E(X{ + Xž). (3) Find V(X1 + X2).
Example #2: A die is rolled. Assume that a random variable X represents the outcomes of this experiment. Construct a probability distribution table and represent this probability distribution graphically. (Use the x-axis for values of X and the y-axis for P(X)). Example #3: A coin is tossed 3 times. Suppose that the random variable X is defined as the number of heads. Construct a probability distribution of X and represent this probability distribution graphically. (Use the x-axis for values of X and the...
fou-369850 Question Beth is performing an experiment to check if a die is fair. She rolls the die 5 times and records the sequence of numbers she gets. Which of these is an outcome of this experiment? Select all correct answers. Select all that apply: Rolling a die Rolling a die five times Rolling the sequence 1, 1,2, 1,6 Rolling five 4's Rolling the sequence 1, 1,2
Suppose you have a die that has probability p of resulting in the outcome 6 when rolled, where p is a continuous random variable that is uniformly distributed over [O, j]. Suppose you start rolling this die. (The value of p does not change once you start rolling.) Give exact answers as simplified fractions. (a) Compute the probability that the first roll is 6. b) Compute the probability that the first two rolls are both 6. (c) Let Si be...