Complete question :
The random variable x represents the number of tests that a patient entering a hospital will have along with the corresponding probabilities. Find the mean and standard deviation.
x 0 1 2 3 4
P(x) 3/17 5/17 6/17 2/17 1/17
Answer:
1.59 ; 1.09
Step-by-step explanation:
The Mean :
E(X) = Σx*p(x)
(0*3/17) + (1 * 5/17) + (2*6/17) + (3*2/17) + (4*1/17)
= 1.58823
= 1.59
Standard deviation = sqrt(Var(x))
Var(X) = Σx²*p(x) - E(x)²
= {(0^2*3/17) + (1^2 * 5/17) + (2^2*6/17) + (3^2*2/17) + (4^2*1/17)} - 1.59^2
= 3.7058823 - 2.5281
= 1.1777823
Standard deviation = sqrt(1.1777823)
= 1.0852567
= 1.09
