Answer:
Step-by-step explanation:
For a valid probability model for X.
For X=0,1,2,3,4,5,6,7
\small 0\leq P(X)\leq 1 (as P(X) is Probability ; Probability can only between 0 and 1).
On this Count ;
these options are not valid ; 3 and 5
X 0 1 2 3 4 5 6 7
P(X) 0 l0 l0 l0 l0 l0 25 25
X 0 I 2 3 4 5 6 7
P(X) -0.50 0.20 0.20 0.20 0.20 0.20 0.20 0.20
And also for a valid probability model for X.
\small \sum_{X=0}^{7}P(X) =1
For option 1:
\small \sum_{X=0}^{7}P(X) =0.125+0.125+0.125+0.125+0.125+ 0.125+0.125+0.125=1
Option1 satisfies both the conditions
Option 2 :
\small \sum_{X=0}^{7}P(X) =0.10+0.05+0.10+0.20+0+ 0.10+0.20+0.25=1
Option 2 satisfies both the conditions
For Option 4,
\small \sum_{X=0}^{7}P(X) =0.10+0.15+0.20+0.25+0.30+ 0.35+0.40+0.45=2.2\small \sum_{X=0}^{7}P(X) =2.2\neq 1
Hence option 4 does not satisfy condition 2
SO , the correct answer is option 1 and 2
X 0 1 2 3 4 5 6 7
PX) 0.125 0.125 0.125 O.125 0.125 0.125 0.125 0.123
X 0 1 2 3 4 5 6 7
PX) 0.10 0.05 0.10 0.20 0 0.10 0.20 0.25
