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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

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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).

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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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