Page 46 - Math SL HB Sem 3

6.18: D ONS

( l)Discrete Random Variables:

A random variables is a numerical variate rvhose vatue depenG on chance-
Let X have the follorving properties:
(a) it is a discrete variable and can take on!- values x',xar_,xn;
(b)the probabilities associated with these vlues are pp pz-_, p.
P(X =x,)= p,

P(X:x,)= p,
Where

P(X:x")- p.

Then, X is a discrete random variable if p, + p2+...+ p, =l

This can be written, IP(X = x) = I

Example:
trt X be the discrete variahle ' the number of fours obtained when t*.o dice are thrown'-Show
that X is a random variable,i.e, that the sum olthe probabilities is I-llustrate the probabilig
distribution on a diagram.

Example: Q ard +k< ol l.* hutnbctcd L at 3
Two unbiased spinners. one numbered 1,2,{are spun.X (the random variable) is the sum of
the trvo results-
a) Tabulate the distribution of X-
b) Find P(x > 5)
c)State the mode-
d) The experiment is rcpeated 60 times.Give the expected irequency distriburion of X.

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