Page 2 - XII-CH13-LESSON NOTES
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12. Random variablen t random variable is a real valued function wh ose domain is tyh e sample space of
a random experimenty.
x nx nx n....x
13. Probability: distyributionn If a random variable X tyakes values 1 2 3 n wityh respective
p np np n....np
probabilities 1 2 3 n tyh en
X x 1 x 2 x 3 …. x n
P(X) p 1 p 2 p 3 …. p n
is known as tyh e probability: distyribution of X.
14. Sum of probabilities in a probability: distyribution is alwa:s 1.
15. Mean (also called expectyed value) of a probability: distyribution is given b:
(p x ) E(x) (p x )
Mean i i n i.e. i i
16. Variance of probability: distyribution is given b:
2
2
(p x ) ( ) 2
i i
2
and styandard deviation =
17. Bernoulli tyrialsn Diferenty tyrials of a random experimenty are called Bernoulli tyrials if
(i) Th e number of tyrials n is fnitye.
(ii) Each tyrial h as exactyl: tywo outycomes- success and failure (non-success) and we h ave
P(success) + P (failure)=1
(iii) Th e tyrials are independenty
(iv) Th e probability: of success remains same for each tyrial denotyed b: p and tyh aty of failure is
denotyed b: q and p + q = 1.
18. Binomial distyributionn If nn pn q are respectivel: number of tyrialsn probability: of success and
probability: of failuren tyh en probability: of r successes
r n r
P(r) n C p q n r 0n1n2n...nn .
r
(q p) n
and binomial distyribution is given b:
n and p are called parametyers of binomial distyribution
