# Solve the following problem : Let X denote the reaction temperature in Celsius of a certain chemical process. Let X have the p. d. f. f(x) = {110 for-5≤x<50otherwise.Compute P(X < 0). - Mathematics and Statistics

Sum

Solve the following problem :

Let X denote the reaction temperature in Celsius of a certain chemical process. Let X have the p. d. f.

f(x) = {((1)/(10),  "for" -5 ≤ x < 5),(0, "otherwise".):}
Compute P(X < 0).

#### Solution

P(X < 0) = int_(-5)^0 f(x)*dx

= (1)/(10) int_(-5)^0 1*dx

= (1)/(10)[x]_(-5)^0

= (1)/(10)(0 + 5)

= (1)/(2).

Concept: Probability Distribution of a Continuous Random Variable
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