# math, probability

13. Exercise: Convergence in probability:

a) Suppose that Xn is an exponential random variable with parameter lambda = n. Does the sequence {Xn} converge in probability?

b) Suppose that Xn is an exponential random variable with parameter lambda = 1/n. Does the sequence {Xn} converge in probability?

c) Suppose that the random variable in the sequence {Xn} are independent, and that the sequence converges to some number a, in probability.
Let {Yn} be another sequence of random variables that are dependent, but where each Yn has the same distribution (CDF) as Xn. Is it necessarily true that the sequence {Yn} converges to a in probability?

1. 👍
2. 👎
3. 👁
1. a) yes
b) no
c) yes

1. 👍
2. 👎
2. y
n
n

1. 👍
2. 👎
3. 142n=47 find n

1. 👍
2. 👎

## Similar Questions

1. ### STATISTICS

Consider a binomial random variable where the number of trials is 12 and the probability of success on each trial is 0.25. Find the mean and standard deviation of this random variable. I have a mean of 4 and a standard deviation

2. ### Probability

Problem 1. Starting at time 0, a red bulb flashes according to a Poisson process with rate λ=1 . Similarly, starting at time 0, a blue bulb flashes according to a Poisson process with rate λ=2 , but only until a nonnegative

3. ### mathematics, statistics

You observe k i.i.d. copies of the discrete uniform random variable Xi , which takes values 1 through n with equal probability. Define the random variable M as the maximum of these random variables, M=maxi(Xi) . 1.) Find the

4. ### math

Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter λ (lambda) = 0.5. What's the probability that a repair takes less than 5 hours? AND what's the

1. ### Statistics

A random variable is normally distributed with a mean of 50 and a standard deviation of 5. b. What is the probability that the random variable will assume a value between 45 and 55 (to 4 decimals)? c. What is the probability that

2. ### probability

Let K be a discrete random variable that can take the values 1 , 2 , and 3 , all with equal probability. Suppose that X takes values in [0,1] and that for x in that interval we have fX|K(x|k)=⎧⎩⎨1,2x,3x2,if k=1,if k=2,if

3. ### Math

Suppose a baseball player had 211 hits in a season. In the given probability distribution, the random variable X represents the number of hits the player obtained in the game. x P(x) 0 0.1879 1 0.4106 2 0.2157 3 0.1174 4 0.0624 5

4. ### Statistics

In a study by Peter D. Hart Research Associates for the Nasdaq Stock Market, it was determined that 20% of all stock investors are retired people. In addition, 40% of all adults invest in mutual funds. Suppose a random sample of

1. ### probability

Problem 2. Continuous Random Variables 2 points possible (graded, results hidden) Let 𝑋 and 𝑌 be independent continuous random variables that are uniformly distributed on (0,1) . Let 𝐻=(𝑋+2)𝑌 . Find the probability

2. ### Probability

Question:A fair coin is flipped independently until the first Heads is observed. Let the random variable K be the number of tosses until the first Heads is observed plus 1. For example, if we see TTTHTH, then K=5. For K=1,2,3...K,

3. ### statistics MIT

2 Let X1,…,Xn be i.i.d. random variable with pdf fθ defined as follows: fθ(x)=θxθ−11(0≤x≤1) where θ is some positive number. (a) Is the parameter θ identifiable? Yes No (b) Compute the maximum likelihood estimator

4. ### Statistics

A person's level of blood glucose and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x