A die is thrown twice. Let X1 and X2 denote the outcomes, and define random variable X to be the minimum of X1 and X2. Determine the distribution of X.

Respuesta :

Answer:

Step-by-step explanation:

Given that a die is thrown twice.  

X1, X2 are the outcomes in 2 throws

X1 = minimum of two

X1 can be either 1 or 2...6

Total outcomes are 36.

For x1 =1, fav ourable outcomes are (1,1) (1,2)...(1,6) (6,1)...(2/,1)= 11

P(X1=1) = [tex]\frac{11}{36}[/tex]\

P(X1=2) =Prob for one die showing two and other die showing 2 to 6

= [tex]\frac{9}{36}[/tex]

P(x1=3) = Prob for one die showing three and other die showing 3 to 6

=[tex]\frac{7}{36}[/tex]

thus we find that probability is reducing by 2 in the numerator

P(x1=4) = 5/36 followed by 3/36 for 5 and 1/36 for 6