Given-a-random-variable-X-of-image-set-X-1-1-2-with-probabilities-P-X-1-e-a-P-X-1-e-b-and-P-X-2-e-c-where-a-b-and-c-are-in-an-Arithmetic-Progression-Assuming-the-mathematical-expec

Question Number 87643 by Ar Brandon last updated on 05/Apr/20

G i v e n a r a n d o m v a r i a b l e X o f i m a g e s e t

X (Ω) = [1; - 1; 2] w i t h p r o b a b i l i t i e s P (X = 1) = e^{a},

P (X = - 1) = e^{b}, a n d P (X = 2) = e^{c} w h e r e a, b, a n d c

a r e i n a n A r i t h m e t i c P r o g r e s s i o n .

A s s u m i n g t h e m a t h e m a t i c a l e x p e c t i o n E (X) o f X

i s e q u a l t o 1 .

1 \cdot S u p p o s e t h e c o m m o n d i f f e r e n c e o f t h e A r i t h m e t i c P r o g r e s s i o n i s r

a \cdot D e t e r m i n e t h e e x a c t v a l u e s o f t h e r e a l n u m b e r s a, b, a n d c .

b . S h o w t h a t t h e v a r i a n c e V (X) o f X i s e q u a l t o \frac{22}{7} .