[Probability Theory] Commonly used continuous distributions (1)

multiple choice

1. Suppose random variable X~N(μ, 16) , Y~N(μ, 25), then ().
   A. For any μ, there is P{X≤μ-4}= P{Y≥μ+5}.
   B. For any μ, there is P{X≤μ-4}<P{Y≥μ+5 }.
   C. Only for individual values ​​of μ, P{X≤μ-4}=P{Y≥μ+5}.
   D. For any μ, P{X≤μ-4}>P{Y ≥μ+5}
   【Correct answer: A】

2. Let the density function of random variable X be f(x)= $C{e}^{-x^2+2x}$, then the constant C=().
   A.$\frac{2}{\sqrt{\pi e}}$
   B. $\frac{1}{\sqrt{2\pi e}}$
   C. $\frac{1}{\sqrt{\pi e}}$
   D. $\frac{1}{\sqrt{2p.m}}$
   【Correct answer: C】

3. Suppose the random variable X~N(μ, σ²), then the probability P{|X-μ|>σ}=().
   A. Has nothing to do with μ, increases with the increase of σ.
   B. Has nothing to do with μ, decreases with the increase of σ.
   C. Has nothing to do with σ, increases with the increase of μ.
   D. Has nothing to do with μ, σ is irrelevant.
   【Correct answer: D】

4. Suppose the random variable X~N(0,σ²), then when σ=(), the probability P{1<X<3} is the largest.
   A. 2
   B. $\ln 3$
   C. $\frac{2}{\sqrt{\ln 3}}$
   D. $\frac{1}{\sqrt{\ln 3}}$
   【Correct answer: C】

5. Suppose random variable. X~N(0, σ²), then there are () for any real number x.
   A. P{X<x}=P{X>-x}
   B. P{X<x}=P{X>x}
   C. P{X<x}≥P{X>-x}
   D. P {X<x}≥P{X>x}
   【Correct answer: A】