Question

The median of a continuous random variable having distribution function F is that value m such that F(m) = 1/2 . That is, a random variable is just as likely to be larger than its median as it is to be smaller. The mode of a continuous random variable having pdf f(x) is the value of x for which f(x) attains its maximum. Find the median and the mode of X if X is(a) uniformly distributed over (a, b)(b) normal with parameters μ, σ2(c) exponential with parameter λ

Answer 1

Answer:

Step-by-step explanation:

To find median and mode for

a) In a uniform distribution median would be

(a+b)/2 and mode = any value

b) X is N

we know that in a normal bell shaped curve, mean = median = mode

Hence mode = median = $\mu$

c) Exponential with parameter lambda

Median = $\frac{ln2}{\lambda }$

Mode =0