A random experiment was conducted where a Person A tossed five coins and recorded the number...

A random experiment was conducted where a Person A tossed five coins and recorded the number of “heads”. Person B rolled two dice and recorded the sum the two numbers. Simulate this scenario (use 10000 long columns) and answer questions 10 to 13.

Hint: check Lectures 26 and 27 in the Book.

10. Which of the two persons (A or B) is more likely to get the number 4?

a. Person A
b. Person B
c. Not possible to determine

11. Which of the two persons will have higher Median among their outcomes?

a. Person A
b. Person B
c. Not possible to determine

12. What is the probability that person B obtains number 5 or 6?

a. About 15%
b. About 25%
c. About 35%
c. About 55%

13. Which of the persons has higher probability of getting the number 3 or smaller?

a. Person A
b. Person B
c. Not possible to determine

Expert Solution

orchestra answered 2 years ago

random experiment was conducted where a Person A tossed five coins and recorded the number of...

random experiment was conducted where a Person A tossed five coins and recorded the number of “heads”. Person B rolled two dice and recorded the average the two numbers. Simulate this scenario (use 10000 long columns) and answer questions 10 to 13. Hint: check Lectures 26 and 27 in the Book. 10. Which of the two persons (A or B) is more likely to get the number 5? a. Person A b. Person B c. Not possible to determine 11....

Two coins are tossed at the same time. Let random variable be the number of heads...

Two coins are tossed at the same time. Let random variable be the number of heads showing. a) Construct a probability distribution for b) Find the expected value of the number of heads.

Five coins were simultaneously tossed 1000 times and at each toss, the number of heads was...

Five coins were simultaneously tossed 1000 times and at each toss, the number of heads was observed. The number of tosses during which 0, 1, 2, 4, and 5 heads were obtained are shown in the table below. Convert the given frequency distribution to probability distribution find the expected value. Number of heads per toss: 0 1 2 3 4 5 Number of tosses : 38 144 342 287 164 25

1. Suppose four distinct, fair coins are tossed. Let the random variable X be the number...

1. Suppose four distinct, fair coins are tossed. Let the random variable X be the number of heads. Write the probability mass function f(x). Graph f(x). 2. For the probability mass function obtained, what is the cumulative distribution function F(x)? Graph F(x). 3. Find the mean (expected value) of the random variable X given in part 1 4. Find the variance of the random variable X given in part 1.

Two fair coins and a fair die are tossed. Find the sample space of the experiment...

Two fair coins and a fair die are tossed. Find the sample space of the experiment (10 pts); Find the probabilities of the following events: A- ”the die shows 2 or 3” (5 pts); B- ”one of the coins is head, the other - tail, and the die shows an odd number” (5 pts). Are the events A and B independent? (5 pts). Give proofs.

4 fair coins are tossed. Let X be the number of heads and Y be the...

4 fair coins are tossed. Let X be the number of heads and Y be the number of tails. Find Var(X-Y) Solution: 3.5 Why?

Consider an experiment where fair die is rolled and two fair coins are flipped. Define random...

Consider an experiment where fair die is rolled and two fair coins are flipped. Define random variable X as the number shown on the die, minus the number of heads shown by the coins. Assume that all dice and coins are independent. (a) Determine f(x), the probability mass function of X (b) Determine F(x), the cumulative distribution function of X (write it as a function and draw its plot) (c) Compute E[X] and V[X]

1. Four coins are tossed 11 times. The number of heads is counted and the following...

1. Four coins are tossed 11 times. The number of heads is counted and the following data is reported: 4, 3, 2, 0, 3, 3, 1, 2, 3, 2, 1. Calculate the following sample statistics. Be sure to provide a formula for your answer. a. Sample mean? b. Sample median? c. Sample mode? d. Sample range? e. Sample variance?

1- Three coins are tossed once. (a) Find the number of macrostates. Explain. (b) Find the...

1- Three coins are tossed once. (a) Find the number of macrostates. Explain. (b) Find the number of microstates. Explain. (c) What is the probability of getting at least one head? Explain. (d) What is the probability of getting one tail? Explain. (e) What is the probability of getting the same face? Explain

Suppose a coin is tossed 100 times and the number of heads are recorded. We want...

Suppose a coin is tossed 100 times and the number of heads are recorded. We want to test whether the coin is fair. Again, a coin is called fair if there is a fifty-fifty chance that the outcome is a head or a tail. We reject the null hypothesis if the number of heads is larger than 55 or smaller than 45. Write your H_0 and H_A in terms of the probability of heads, say p. Find the Type I...

Question