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

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 =

c) Exponential with parameter lambda

Median =

Mode =0

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)