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IMM probability and statistics Quizz 1 Flashcards | StudBud

Explore/IMM probability and statistics Quizz 1

IMM probability and statistics Quizz 1

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Questions 8

Answers

1
Let Z denote a centered normal random variable with variance 4
(Z/2)2 follows a Chi-square distribution with 1 degree
(Z-2)2 follows a Chi-square distribution
E(Z4)=4
Z2 follows a Chi-square distribution with 1 degree
2
A Binomial distribution of parameters n and p is the sum of n independent Bernoulli of parameter p
True
False
3
Let X be a Student distribution with 2 degree of freedom
The mean of X is 0
The distribution of X is symmetric with respect to 2
The mean of X is 2
4
Let X be a real random variable with Poisson distribution of parameter λ
E(X)=Var(X)=λ
E(X2)=Var(X)=λ
E(X)=Var(X)=λ2
5
One can construct a Student distribution with two independent normal distributions
True
False
6
Let Z denote a standard normal random variable
Z2 follows a Chi-square distribution with 1 degree
Z2 follows a Chi-square distribution with 2 degree
Z1/2 follows a normal distribution
Z2 follows a Student distribution with 1 degree
7
Let X be a Student distribution with n>0 degree of freedom
Quantile z0.05 of order 0.05 is -z0.95 (z0.95, quantile of order 0.95)
The standard deviation is 1
P(X\le1)=1- P(X\ge-1)
8
Let Z denote a standard normal random variable
P(Z\le-1.2)=P(Z\ge1.2)=0.1151
The distribution is symetric with respect to 1
The median may be different to the mean
The median and the mean are 0.5