Respuesta :
Answer:
a. P(X = 2) = 0.2
b. P(X = 3) = 0.3
c. P(X > 2.5) = 0.7
d. P(X = 1) = 0.1
e. Mean = 3
f. Variance = 1
Step-by-step explanation:
As given,
Probability mass function (pmf) = [tex](\frac{1}{2})(\frac{x}{5} ) = \frac{x}{10}[/tex]
Now,
a. P(X = 2) = [tex]\frac{2}{10}[/tex] = 0.2
b. P(X = 3) = [tex]\frac{3}{10}[/tex] = 0.3
c. P(X > 2.5) = P(X = 3) + P(X = 4) = [tex]\frac{3}{10} + \frac{4}{10}[/tex] = 0.3 + 0.4 = 0.7
d. P(X = 1) = [tex]\frac{1}{10}[/tex] = 0.1
e. Mean = E(X) = [tex]1.\frac{1}{10} + 2.\frac{2}{10} + 3.\frac{3}{10} + 4.\frac{4}{10}[/tex] = 0.1 + 0.4 + 0.9 + 1.6 = 3
f. Variance = E(X²) - [ E(X) ]² = [tex]1^{2} .\frac{1}{10} + 2^{2} .\frac{2}{10} + 3^{2} .\frac{3}{10} + 4^{2} .\frac{4}{10}[/tex] - [3]²
= 0.1 + 0.8 + 2.7 + 6.4 - 9
= 10 - 9 = 1
∴ we get
a. P(X = 2) = 0.2
b. P(X = 3) = 0.3
c. P(X > 2.5) = 0.7
d. P(X = 1) = 0.1
e. Mean = 3
f. Variance = 1
