How to solve this

[mrittik]

Suppose a random variable X takes values -2, 0, 1 and 4 with probabilities 0.4, 0.1, 0.3 and 0.3 respectively

a) The unique median of the dist is 1.
b) The unique median of the dist is 0.
c) The unique median of the dist lies b/w 0 and 1.
d) The dist has multiple medians.

What is the concept of this qsn?

[The Villain]

The ans is d
Consider, P(X<=0)=.5   P(X>=0)=.6
P(X<=1)=.8          P(X>=1)
Hence multiple median.

[mrittik]

Thanks Ron. But sorry I can't understand the concept...plz elaborate amigo

[Sumit]

 For each random variable X, a median of the distribution of X is defined as number m such that
pr(X<=m)>=1/2 & pr(X>=)>=1/2.

[Dreyfus]

Mritik are u sure that u hv written the correct probabilities? As its not legitimate PDF..as p sums to 1.1!

[Homer Simpson]

exactly, can you re-check mrittik?

[The Villain]

Its dse 2010 quest...he has mistyped!!

[mrittik]

sry the last one would be 0.2

[Homer Simpson]

wouldnt it be (a) or maybe (c) then?? can someone correct me on this?

[Dreyfus]

@tsuki...if xo is median of discrete PDF then it should satisfy
 P(X<=xo)>=0.5
And P(X>=xo)>=0.5
Both xo=1 and 0 satisfies this hence median is 0 and 1

[Homer Simpson]

ooh, and what about anything between 0 and 1? say X = 3/4 I know its not strictly mentioned in the discrete PDF but if we add up the probabilities more than or less than, we should end up with 1/2?

[X]

Consider the given probabilities as frequencies: So, the problem is find the median of : -2,-2,-2,-2,0,1,1,1,4,4. And we can see that 0 and 1 are both eligible for median as well as anything between them.

[mrittik]

More solid foundation concept needed....thanks all of you who are thinking abt this problem....tobe tsuki tomar approach ta aro amake confuse kore dilo

[Homer Simpson]

@mrittik: Arrey ami concept jaani naa, ejonno jigesh korchi :P even i am confused rei

[X]

See DeGeroot. Nicely explained.

[kangkan]

@ron? which year?

[Anakin Skywalker]

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[mrittik]

@Anirudh...this median can't be 0.5 because of the probability dist of the values.....Vaibhav has approached in a right way