Find the value of p in each of these probability distributions
x 5 7 9 11 13
P(X=x) p p p 0.12 0.04
x -2 0 1 3
P(X=x) 2/9 1/9 p 2/9
x -4 -1 2 5 8
P(X=x) 0.12 0.24 p 2p 0.07
To find the value of p in each of these probability distributions, you need to understand that the sum of the probabilities for all possible values of x should equal 1.
For the first probability distribution:
You are given the values of x and their respective probabilities. Since two probabilities are given as p, you can set up an equation:
p + p + p + 0.12 + 0.04 = 1
Combining like terms, the equation becomes:
3p + 0.16 = 1
Solving for p:
3p = 1 - 0.16
3p = 0.84
p = 0.84 / 3
p = 0.28
So, the value of p in the first probability distribution is 0.28.
For the second probability distribution:
Again, you are given the values of x and their respective probabilities. One probability is given as p. Set up an equation:
2/9 + 1/9 + p + 2/9 = 1
Combining like terms, the equation becomes:
4/9 + p = 1
Solving for p:
p = 1 - 4/9
p = 9/9 - 4/9
p = 5/9
So, the value of p in the second probability distribution is 5/9.
For the third probability distribution:
Once again, you are given the values of x and their respective probabilities. Two probabilities are given as p. Set up an equation:
0.12 + 0.24 + p + 2p + 0.07 = 1
Combining like terms, the equation becomes:
3.36p + 0.43 = 1
Solving for p:
3.36p = 1 - 0.43
3.36p = 0.57
p = 0.57 / 3.36
p ≈ 0.1696
So, the value of p in the third probability distribution is approximately 0.1696.