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multiple choice
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Let the density function of random variable X be
f ( x ) = { 1 / 3 , 0 < x < 1 , 2 / 9 , 3 < x < 6 , 0 , others . f(x)= \begin{cases} 1/ 3,&0<x<1, \\ 2/9,&3<x<6, \\ 0,&others. \end{cases}f(x)=⎩⎪⎨⎪⎧1/3,2/9,0,0<x<1,3<x<6,others.
Known P { X > k } = 2 3 P \{ X>k \} = \frac {2}{3}P{ X>k}=32, then the value range of k is ().
A. [1, ∞)
B. [1,3]
C. [2,3]
D. [2, ∞)
【Correct answer: B】 -
Suppose the density function of random variable X is f(x), then the density function of a certain random variable in the following functions must be ().
A. 2f(x)
B. f(2x)
C. f(1-x)
D. 1-f(x)
【Correct answer: C】 -
Suppose the density function of random variable X is f(x) is an even function, and F(x) is the distribution function of X, then there must be ().
A. F(x)=F(-x)
B. F(x)-F(-x)=1
C. f(0)=0.5
D. F ( − x ) + ∫ 0 xf ( t ) dt = 0.5 F(-x)+ \int _{0}^{x}f(t)dt=0.5F(−x)+∫0xf(t)dt=0 . 5
【Correct answer: D】 -
Suppose the density function of continuous random variable X is f(x), and F(x) is the distribution function of X, then the following options must be true ().
A. 0≤f(x)≤1
B. F(0)=P{X=0}
C. P{X<x}<F(x)
D. P{X<x}=F(x)
【 Correct answer: D] -
Let the density function of random variable X be
f ( x ) = { λ e − λ x , x > 0 , 0 , otherx , f(x)= \begin{cases} \lambda e^{-\lambda x},&x >0, \\ 0,&otherx, \end{cases}f(x)={ λe−λx,0,x>0,otherx,,
Y obeys the parameter λ \lambdaλ Poisson distribution, known
P(X>1)=0.5, then P{Y>2}=().
A. 0.5
B.2 − 2 ln 2 − ( ln 2 ) 2 4 \frac {2-2 \ln 2-( \ln 2)^{2}}{4}42−2ln2−(ln2)2
C. 0.1
D. ln 2 \ln2 ln2
[Correct answer: B] -
Let the random variable X~U(0,1), record the event A={0<X<0.5}, B={0.25< X<0.75}, then ().
A. Events A and B are mutually incompatible
B. A⊂B
C. Events A and B are opposed
D. Events A and B are independent of each other
【Correct answer: D】