Suppose we need to pick two numbers from {1,2,3,4,...,100} uniformly at random (you might choose the...

Suppose we need to pick two numbers from {1,2,3,4,...,100} uniformly at random (you might choose the same number twice). What is the probability that the sum of the two picked numbers is divisible by 5?

Expert Solution

orchestra answered 2 years ago

1.Suppose n and k are two positive integers. Pick a uniformly random lattice path from (0,...

1.Suppose n and k are two positive integers. Pick a uniformly random lattice path from (0, 0) to (n, k). What is the probability that the first step is ‘up’?

2) Suppose I use a random numbers table to randomly choose 900 numbers between 0 and 100....

2) Suppose I use a random numbers table to randomly choose 900 numbers between 0 and 100. In this particular sample, the mean of the 900 numbers is 50 and the standard deviation is 30. a)Approximately, what proportion of the 900 numbers should fall between 20 and 80 (inclusive)? b)Suppose each student in Static (class size = 140) repeats the experiment described above and computes the mean of his or her 900 numbers. Based on the information given above, estimate the...

Suppose we have a random variable X that is uniformly distributed between a = 0 and...

Suppose we have a random variable X that is uniformly distributed between a = 0 and b = 100. What is σ X? a. 0.913 b. 0.833 c. 50 d. 7.071

Appendix B.4 is a table of random numbers that are uniformly distributed. Hence, each digit from...

Appendix B.4 is a table of random numbers that are uniformly distributed. Hence, each digit from 0 through (including) 9 has the same likelihood of occurrence. (Round your answers to 2 decimal places.) a) Compute the population mean and standard deviation of the uniform distribution of random numbers. Population mean Population Standard Deviation b) Assume that 10 random samples of five values are selected from a table of random numbers. The results follow. Each row represents a random sample....

Suppose we define a relation on the set of natural numbers as follows. Two numbers are...

Suppose we define a relation on the set of natural numbers as follows. Two numbers are related iff they leave the same remainder when divided by 5. Is it an equivalence relation? If yes, prove it and write the equivalence classes. If no, give formal justification.

Propose two of your own random number generation schemes. Please generate 100 random numbers ?? (?...

Propose two of your own random number generation schemes. Please generate 100 random numbers ?? (? = 1,2, … ,100) for each scheme and show the results on the same plot for comparison (i.e., x-axis of the plot will show the index ? and y-axis will show the generated random numbers ??. You can use different colors and/or symbols to distinguish one sequence from the other). Discuss which scheme will be preferred.

Suppose you choose a coin at random from an urn with 3 coins, where coin i...

Suppose you choose a coin at random from an urn with 3 coins, where coin i has P(H) = i/4. What is the pmf for your prior distribution of the probability of heads for the chosen coin? What is your posterior given 1 head in 1 flip? 2 heads in 2 flips? 10 heads in 10 flips?Hint: Compute the odds for each coin first.

Pick two cards at random from a well-shuffled deck of 52 cards (pick them simultaneously so...

Pick two cards at random from a well-shuffled deck of 52 cards (pick them simultaneously so they are not the same card). There are 12 cards considered face cards. There are 4 cards with the value 10. Let X be the number of face cards in your hand. Let Y be the number of 10's in your hand. Explain why X and Y are dependent.

This is a standard deviation contest. You must choose four numbers from the whole numbers 0...

This is a standard deviation contest. You must choose four numbers from the whole numbers 0 to 10, with repeats allowed. Step 1: Choose four numbers that have the smallest possible standard deviation. What is the numerical value of s in this case? Give your answer as a whole number (meaning no decimal places). Step 2: Is there more than one possibility for choosing four numbers that have the smallest possible standard deviation? No. Yes. Step 3: Choose four numbers...

6. Suppose that you choose a student at random, and let the random variable “H” represent...

6. Suppose that you choose a student at random, and let the random variable “H” represent the student’s studying time (in hours) last week. Suppose that “H” has a uniform distribution on the interval (25, 35). If you randomly select 10 students and that each person’s studying time follows this same probability distribution, independently from person to person, determine the probability that at least two of the students studied for more than 32 hours last week.

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