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

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AlonsoDehner AlonsoDehner · Answer 1 · 2019-12-04T10:27:34+01:00

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 = [tex]\mu[/tex]

c) Exponential with parameter lambda

Median = [tex]\frac{ln2}{\lambda }[/tex]

Mode =0

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MrRoyal MrRoyal · Answer 2 · 2022-04-03T18:10:31+02:00

The median of a distribution is the middle value while the mode is the highest occuring value

The median (M) of a uniform distribution is:

[tex]M = \frac{a +b}2[/tex]

A uniform distribution has no mode

For a normal distribution with the given parameters, we have:

Median = Mean = Mode = μ

Hence, the median and the mode are μ

For an exponential distribution with the given parameter, we have:

[tex]Median = \frac{\ln 2}{\lambda}[/tex]

The mode of an exponential distribution is 0