probability

Question 1

pmf of uniform discrete distribution

Answer 1

1 / (b-a+1)

Question 2

expectation of uniform discrete distribution

Answer 2

(a+b) / 2

Question 3

variance of uniform discrete distribution

Answer 3

( (b - a + 1)^2 - 1 ) / 12

Question 4

pmf of bernoulli distribution

Answer 4

f(0) = p, f(1) = 1-p

Question 5

expectation of bernoulli distribution

Answer 5

p

Question 6

variance of bernoulli distribution

Answer 6

p(1-p)

Question 7

pmf of binomial distribution

Answer 7

(n x) p^x (1-p)^(n-x)

Question 8

expectation of binomial distribution

Answer 8

np

Question 9

variance of binomial distribution

Answer 9

np(1-p)

Question 10

pmf of geometric distribution

Answer 10

p (1-p)^(x-1)

Question 11

expectation of geometric distribution

Answer 11

1 / p

Question 12

variance of geometric distribution

Answer 12

1/p - 1/p^2

Question 13

pmf of poisson distribution

Answer 13

(v^x / x!) e^(-v)

Question 14

expectation of poisson distribution

Answer 14

v

Question 15

variance of poisson distribution

Answer 15

v^2

Question 16

pdf of uniform distribution

Answer 16

1/(b-a) if x in (a,b)

Question 17

expectation of uniform distribution

Answer 17

(a+b) / 2

Question 18

variance of uniform distribution

Answer 18

(b - a)^2 / 12

Question 19

pdf of exponential distribution

Answer 19

v e^(-vx) if x>0

Question 20

expectation of exponential distribution

Answer 20

1 / v

Question 21

variance of exponential distribution

Answer 21

1 / v^2

Question 22

pdf of gamma distribution

Answer 22

(b^a / G(a)) x^(a-1) e^(-bx) if x>0

Question 23

expectation of gamma distribution

Answer 23

a / b

Question 24

variance of gamma distribution

Answer 24

a / b^2

Question 25

pdf of normal distribution

Answer 25

(1 / o |2pi) e^( -(x-u)^2 / 2o^2 )

Question 26

expectation of normal distribution

Answer 26

u

Question 27

variance of normal distribution

Answer 27

o^2