A fair (6-sided) die is rolled once, generating a number N. If the number N is...
A fair (6-sided) die is rolled once, generating a number N. If the number N is even, then a fair coin is tossed N + 1 times. If the number N is odd, then a fair coin is tossed 2N times. Let X be the number of heads obtained. Compute E(X). Give a numerical answer as a reduced fraction or a decimal expression accurate to at least 4 decimal places.
Homework Answers
Add Answer to:
A fair (6-sided) die is rolled once, generating a number N. If
the number N is...
A fair 6-sided die is rolled and you note whether the number facing up is even...
A fair 6-sided die is rolled and you note whether the number facing up is even or odd. If an even number is rolled then a fair coin is flipped three more times and the number of heads is noted. But if an odd number is rolled then the coin is flipped only twice more and the number of tails is noted. How many possible outcomes are there for this experiment? (a) 43 (b) 20 (c) 7 (d) 45 (e)...
7. (3 points) Given a fair 6-sided die. Each time the die is rolled, the probabilities...
7. (3 points) Given a fair 6-sided die. Each time the die is rolled, the probabilities of rolling any of the numbers from 1 to 6 are all equal. 1) If it is rolled once and let A be the event of rolling a number larger than 3 and B be the event of rolling an odd number. What is P(AV B)? 2) If it is rolled three times, what is the probability that the same number shows up in...
3. A fair coin is tossed, and a fair six-sided die is rolled. What is the...
3. A fair coin is tossed, and a fair six-sided die is rolled. What is the probability that the coin come up heads and the die will come up 1 or 2? A. 1/2 B. 1/4 C. 1/6 E. 1/3
If a 25- sided fair die that is numbered from 1 to 25 is rolled once,...
If a 25- sided fair die that is numbered from 1 to 25 is rolled once, find the probability of getting (a) a number less than 5 or at least 20. Show your work in details. (b) a number less than 5 and at least 20. Show your work in details (c) an even number. Show your work in details (d) an odd number. Show your work in details
1. Suppose a fair six-sided die is tossed, with N being the resulting number on the...
1. Suppose a fair six-sided die is tossed, with N being the resulting number on the uppermost face. Given N, a fair coin is tossed independently until N heads are recorded. Let X be the total number of tails recorded. a. What is the pmf of N? (5 pts) b. Given N = 3, what is the distribution of X? (10 pts) c. What is Pr(X = 1)? (10 pts) d. What is E(X)? (10 pts)
Please answer questions a b and c I0 a) If a fair die is rolled 22...
Please answer questions a b and c
I0 a) If a fair die is rolled 22 times, what is the probability that a 6 is obtained exactly 3 times? (b) If a fair die is rolled, what is the probability that the third time that a 6 is obtained is on the tenth roll? (c) If a fair coin is tossed 11 times, what is the prob ability that three or fewer heads are obtained?
A 20-sided fair die and an 8-sided fair die are rolled. What is the probability of...
A 20-sided fair die and an 8-sided fair die are rolled. What is the probability of rolling: exactly a 5 on the first die OR a 2 or larger on the second die? Enter your answer as a reduced fraction. ________________
5. A fair six sided die is rolled 10 times. Let X be the number of...
5. A fair six sided die is rolled 10 times. Let X be the number of times the number '6' is rolled. Find P(X2)
A single six-sided die, whose faces are numbered 1 to 6, is rolled n times. The...
A single six-sided die, whose faces are numbered 1 to 6, is rolled n times. The die is fair, each face is equally likely to land upward when the die is rolled. Let X be the number of times that the number on the upward face of the die is 1. Find the mean and the standard deviation of the random variable X.
Consider the setting where you first roll a fair 6-sided die, and then you flip a...
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).
7. (3 points) Given a fair 6-sided die. Each time the die is rolled, the probabilities of rolling any of the numbers from 1 to 6 are all equal. 1) If it is rolled once and let A be the event of rolling a number larger than 3 and B be the event of rolling an odd number. What is P(AV B)? 2) If it is rolled three times, what is the probability that the same number shows up in...
3. A fair coin is tossed, and a fair six-sided die is rolled. What is the probability that the coin come up heads and the die will come up 1 or 2? A. 1/2 B. 1/4 C. 1/6 E. 1/3
1. Suppose a fair six-sided die is tossed, with N being the resulting number on the uppermost face. Given N, a fair coin is tossed independently until N heads are recorded. Let X be the total number of tails recorded. a. What is the pmf of N? (5 pts) b. Given N = 3, what is the distribution of X? (10 pts) c. What is Pr(X = 1)? (10 pts) d. What is E(X)? (10 pts)
Please answer questions a b and c
I0 a) If a fair die is rolled 22 times, what is the probability that a 6 is obtained exactly 3 times? (b) If a fair die is rolled, what is the probability that the third time that a 6 is obtained is on the tenth roll? (c) If a fair coin is tossed 11 times, what is the prob ability that three or fewer heads are obtained?
5. A fair six sided die is rolled 10 times. Let X be the number of times the number '6' is rolled. Find P(X2)
Most questions answered within 3 hours.
-
Using MARS simulator, write MIPS programs according to
the following scenarios: Receive a positive integer number...
asked 1 hour ago -
An object in front of a concave mirror has a real image that is
11.5 cm...
asked 1 hour ago -
Consider the reaction, C3 H8 + O2 --> CO2 + H2O. How many
moles of O2...
asked 3 hours ago -
You and your opponent both roll a fair die. If you both roll the
same number,...
asked 3 hours ago -
In a study of the accuracy of fast food​ drive-through orders,
Restaurant A had 257 accurate...
asked 3 hours ago -
Identify and describe in detail the four categories of
institutions that could be included in a...
asked 3 hours ago -
In python
class Customer:
def __init__(self, customer_id, last_name, first_name, phone_number, address):
self._customer_id = int(customer_id)
self._last_name =...
asked 3 hours ago -
What is an example of a limitation in implementing a new
ERP system and how it...
asked 3 hours ago -
In a section of 9.7cm of an artery with a radius of 2.6mm there
is a...
asked 3 hours ago -
the two carboxylic acid groups of aspartic acid have different
acidities with pKa values of 2.1...
asked 3 hours ago -
Would CuCO3 aqueous salt combined with calcium chloride
form a solid precipitate? If so, what would...
asked 3 hours ago -
How do ECM Solutions assist in embedding a culture of continuous
improvement in an organization? (Project...
asked 4 hours ago