Answer:
E (Y) = 3
Step-by-step explanation:
If a 4-sided die is being rolled repeatedly; and the odd-numbered rolls (1st 3rd,5th, etc.)
The probability of odd number roll will be, p(T) = [tex]\frac{1}{2}[/tex]
However, on your even-numbered rolls, you are victorious if you get a 3 or 4. Also, the probability of even number roll, p(U) = [tex]\frac{1}{2}[/tex]
In order to calculate: E (Y); We can say Y to be the number of times you roll.
We know that;
E (Y) = E ( Y|T ) p(T) + E ( Y|U ) p(U)
Let us calculate E ( Y|T ) and E ( Y|U )
Y|T ≅ geometric = [tex]\frac{1}{4}[/tex]
Y|U ≅ geometric = [tex]\frac{1}{2}[/tex]
also; x ≅ geometric (p)
∴ E (x) = [tex]\frac{1}{p}[/tex]
⇒ [tex]\frac{Y}{T}[/tex] = 4 ; also [tex]\frac{Y}{U}[/tex] = 2
E (Y) = 4 × [tex]\frac{1}{2}[/tex] + 2 ×
= 2+1
E (Y) = 3
