A random variable X following the Bernoulli distribution with
shape param-
eter p has probability density function (pdf) given by
f(x) =
p
x
(1 − p)
1−x x = 0, 1
0 otherwise
Show that
a) P1
x=0 f(x) = 1 [5 Marks]
b) E[X]=p [5 Marks]
c) Var[X]=p(1-p) [5 Marks]
d) the MGF of X is given by (1 − p) + pet
A random variable X following the Bernoulli distribution with shape param- eter p has probability density...
Suppose the random variable X has probability density function (pdf) - { -1 < x<1 otherwise C fx (x) C0 : where c is a constant. (a) Show that c = 1/7; (b) Graph fx (х); (c) Given that all of the moments exist, why are all the odd moments of X zero? (d) What is the median of the distribution of X? (e) Find E (X2) and hence var X; (f) Let X1, fx (x) What is the limiting...
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The Bernoulli random variable takes values 0 and 1, and has probability function f(x) = px (1 − p)1−x(a) By calculating f(0) and f(1), give a practical example of a Bernoulli experiment, and a Bernoulli random variable. (b) Calculate the mean and variance of the Bernoulli random variable.
The random variable X has probability density function k(x25x-4) 1<x<4 otherwise -{ f(x) 1. Show thatk. (5pts) Find 2. Е (X), (5pts) 3. the mode of X, (5pts) 4. the cumulative distribution function F(X) for all x. (5pts) 5. Evaluate P(X < 2.5). (5pts) 6. Deduce the value of the median and comment on the shape of the distribution (10pts)
Show work. Thanks 2.5.6. The probability density function of a random variable X is given by に " f(x) =10, 0, otherwise (a) Find c. (b) Find the distribution function F(x) (c) Compute P 3)