dear student, we can provide you with a solution of one type of question at a time.
1)
Here First you need to form the probability distribution of X
a)
b) Variance =
c) Standard deviation of X =
We flip a coin. If it is heads we roll a four sided die with sides...
Exercise 10.17. We flip a fair coin. If it is heads we roll 3 dice. If it is tails we roll 5 dice. Let X denote the number of sixes among the rolled dice. (a) Find the probability mass function of X. (b) Find the expected value of X.
You roll a 6-sided die. What is the probability that you will roll either a 3 or a 2? P (3 or 2) = You flip a 2-sided coin. What is the probability that you will get either heads or tails? P (heads or tails) =
You flip a fair coin. On heads, you roll two six-sided dice. On tails, you roll one six-sided dice. What is the chance that you roll a 4? (If you rolled two dice, rolling a 4 means the sum of the dice is 4) O 1 2 3 36 1 2 1 6 + + 1 4 36 1 6 2 2 1 36 + -10 2 . 4 36 + 4 6 2 2
of a fair coin. Also use the binomial formula and compare the two probabilities. For the normal approximation use z (x-H)/a, then use the tables, and for the binomial use (n C x) "(1-0) . Given heads is a success when we flip a coin, a six when we roll a die, and getting an ace when we select a card from a 52-card deck. Find the mean and std. deviation of the total number of successes when we (a)...
Let W be a function that takes the result of a six-sided die roll and multiplies it by 0 if a coin lands Heads, and 1 if it lands Tails. What is the distribution over W? What is the expectation?
Draw a tree diagram displaying all possible outcomes given a roll of a six sided die, a coin flip, then a second coin flip. Examples of possible outcomes are 5H H meaning a roll of a , then a Heads, and a Heads TH meaning a roll of a 1, then a Tails, then a Heads
Consider the setting where you first roll a fair 6-sided die, and then you flip a fair coin the number of times shown by the die. Let D refer to the outcome of the die roll (i.e., number of coin flips) and let H refer to the number of heads observed after D coin flips. (a) Suppose the outcome of rolling the fair 6-sided die is d. Determine E[H|d] and Var(H|d). (b) Determine E[H] and Var(H).
Consider a die with 2 red sides, 2 green sides, and 2 blue sides. Roll the die 5 times, and let X denote the number of times that the die has a red result. Flip a coin 5 times, and let Y denote the number of times that the coin shows “heads." a. Find E(X?Y). b. Find Var?(X?Y).
1) Suppose we have a fair 6 sided die and a coin. a) If we roll the die 4 times, the total number of possible outcomes is? b) If we roll the die 2 times then flip the coin 3 times, the total number of possible outcomes is? Show your calculations.
If you flip a coin and roll a die at the same time, what is the probability of rolling a 5 or 6 and the coin showing heads? Question 3 Unanswered If you flip a coin and roll a die at the same time, what is the probability of rolling a 5 or 6 and the coin showing heads? (answer to 4 decimal places) Type your response