Solution : ( 1.1 )
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Solution : ( 1.2 )
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I. If a variable X has the mean μ and the variance σ, express the following...
X is a normal random variable with mean μ and standard deviation σ. Then P( μ− 1.6 σ ≤ X ≤ μ+ 2.6 σ) =? Answer to 4 decimal places.
2. Let us assume that the population X has the mean μ and the variance σ2 and the population Y h 2σ. If X and Y are independent, express the following quantities by and ơ as the mean u and the variance (2.2) V[X-Y] (2.3) V[2X+3Y] (2.4) VIX-3Y-5]
A discrete random variable X has the following probability distribution: x7778798081 P(x) 0.150.150.200.400.10Compute each of the following quantities. i. P(X = 80) ii. P(x > 80) iii. P(X ≤ 80) iv. The mean, μ of x. v. The variance, σ2 of X. vi. The standard deviation, σ of X.
12 Find 10. Let X be a Gaussian rv with mean μ and variance σ, or pdf-l-e 2ơ . Find E X-E(Xt]. Hint: variable substitution, even or odd integrand.
The following function is probability mass function. f(x) _뿡 5x+5 75 x-0.1.2.3.4 Determine the mean, μ, and variance, σ , of the random variable.
Let X have a normal distribution with mean μ and variance σ ^2 . The highest value of the pdf is equal to 0.1 and when the value of X is equal to 10, the pdf is equal to 0.05. What are the values of μ and σ?
(20 points) Suppose X~N(25, 81). That is, X has a normal distribution with μ-25 and σ-81 la. Find a transformation of X that will give it a mean of zero and a variance of one (ie., standardize X lb. Find the probability that 18 < χ < 26. lc. Supposing Y10 +5X, find the mean of Y ld. Find the variance ofY
A random variable X has a mean μ = 10 and a variance σ2-4. Using Chebyshev's theorem, find (a) P(X-101-3); (b) P(X-101 < 3); (c) P(5<X<15) (d) the value of the constant c such that P(X 100.04
Suppose X is a normal random variable with mean μ = 70 and standard deviation σ = 7. Find b such that P(70 ≤ X ≤ b) = 0.3. HINT [See Example 3.] (Round your answer to one decimal place.) b =
(b) Suppose that the random variable X has a normal distribution with mean μ and standard deviation σ. Which of the following is correct about the value x-μ+.28ơ i. The z-score of x is-0.58. ії. x is approximately .61 standard deviations above the mean. iii. There is approximately 39% chance of getting a value that is larger than x. iv. There is approximately 61% chance of getting a value that is larger than T v. r is approximately the 39th...