Let Y be a uniformly distribution random variable. Find: (a) P(|Y −μ|≤2σ) (b) Use Tchebysheff’s theorem...

Let Y be a uniformly distribution random variable. Find:

(a) P(|Y −μ|≤2σ)
(b) Use Tchebysheff’s theorem to estimate P(|Y − μ| ≤ 2σ).
(c) Use the empirical rule to estimate P (|Y − μ| ≤ 2σ).
(d) How does (b) compare to (a)?
(e) How does (c) compare to (a)?

Expert Solution

I have answered the question below

Please up vote for the same and thanks!!!

Do reach out in the comments for any queries

Answer:

a)

b)

c)

d) & e)

a) is quite close to empirical rule as compared to Tchebysheff's theorem

orchestra answered 1 year ago

Let z be a random variable with a standard normal distribution. Find “a” such that P(|Z|...

Let z be a random variable with a standard normal distribution. Find “a” such that P(|Z| <A)= 0.95 This is what I have: P(-A<Z<A) = 0.95 -A = -1.96 How do I use the symmetric property of normal distribution to make A = 1.96? My answer at the moment is P(|z|< (-1.96) = 0.95

Let z be a random variable with a standard normal distribution. Find P(0 ≤ z ≤...

Let z be a random variable with a standard normal distribution. Find P(0 ≤ z ≤ 0.46), and shade the corresponding area under the standard normal curve. (Use 4 decimal places.)

Let be a continuous random variable that has a normal distribution with μ = 48 and...

Let be a continuous random variable that has a normal distribution with μ = 48 and σ = 8. Assuming , n/N ≤ 0.05, find the probability that the sample mean, x , for a random sample of 16 taken from this population will be more than 45.30 . Round your answer to four decimal places.

Let the random variable X follow a normal distribution with a mean of μ and a...

Let the random variable X follow a normal distribution with a mean of μ and a standard deviation of σ. Let 1 be the mean of a sample of 36 observations randomly chosen from this population, and 2 be the mean of a sample of 25 observations randomly chosen from the same population. a) How are 1 and 2 distributed? Write down the form of the density function and the corresponding parameters. b) Evaluate the statement: ?(?−0.2?< ?̅1 < ?+0.2?)<?(?−0.2?<...

(a) Let X be a binomial random variable with parameters (n, p). Let Y be a...

(a) Let X be a binomial random variable with parameters (n, p). Let Y be a binomial random variable with parameters (m, p). What is the pdf of the random variable Z=X+Y? (b) Let X and Y be indpenednet random variables. Let Z=X+Y. What is the moment generating function for Z in terms of those for X and Y? Confirm your answer to the previous problem (a) via moment generating functions.

2] Let x be a continuous random variable that has a normal distribution with μ =...

2] Let x be a continuous random variable that has a normal distribution with μ = 48 and σ = 8 . Assuming n N ≤ 0.05 , find the probability that the sample mean, x ¯ , for a random sample of 16 taken from this population will be between 49.64 and 52.60 . Round your answer to four decimal places.

Let x be a continuous random variable that has a normal distribution with μ = 60...

Let x be a continuous random variable that has a normal distribution with μ = 60 and σ = 12. Assuming n ≤ 0.05N, where n = sample size and N = population size, find the probability that the sample mean, x¯, for a random sample of 24 taken from this population will be between 54.91 and 61.79. Let x be a continuous random variable that has a normal distribution with μ = 60 and σ = 12. Assuming n...

let the random variable x follow a normal distribution with μ = 50 and σ2 =...

let the random variable x follow a normal distribution with μ = 50 and σ2 = 64. a. find the probability that x is greater than 60. b. find the probability that x is greater than 35 and less than 62 . c. find the probability that x is less than 55. d. the probability is 0.2 that x is greater than what number? e. the probability is 0.05 that x is in the symmetric interval about the mean between...

Let X∼Binomial(n,p) and Y∼Bernoulli(p) be independent random variables. Find the distribution of X+Y using the convolution...

Let X∼Binomial(n,p) and Y∼Bernoulli(p) be independent random variables. Find the distribution of X+Y using the convolution formula

Let ? be a binomial random variable with ? = 9 and p = 0.4. Find:...

Let ? be a binomial random variable with ? = 9 and p = 0.4. Find: ?(?>6) ?(?≥2) ?(2≤?<5) ?(2<?≤5) ?(?=0) ?(?=7) ?? ?2

Question