let-X-1-and-X-2-be-independent-random-variable-of-uniform-distribution-If-it-is-known-that-X-i-uniform-0-1-and-let-S-X-1-X-2-Determine-the-Probability-density-function-from-S-

Tinku Tara June 4, 2023 Probability and Statistics 0 Comments

Question Number 145678 by syamilkamil1 last updated on 07/Jul/21

let X_1 and X_(2 ) be independent random variable of uniform distribution . If it is known that X_i ∼uniform (0,1) and let S = X_1 + X_2 Determine the Probability density function from S!

$${let}\:{X}_{\mathrm{1}} \:{and}\:{X}_{\mathrm{2}\:} \:{be}\:{independent}\:{random}\:{variable}\: \\ $$$${of}\:{uniform}\:{distribution}\:.\:{If}\:{it}\:{is}\:{known}\:{that} \\ $$$${X}_{{i}} \sim{uniform}\:\left(\mathrm{0},\mathrm{1}\right)\:{and}\:{let}\:{S}\:=\:{X}_{\mathrm{1}} \:+\:{X}_{\mathrm{2}} \\ $$$${Determine}\:{the}\:{Probability}\:{density}\:{function} \\ $$$${from}\:{S}! \\ $$

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let-X-1-and-X-2-be-independent-random-variable-of-uniform-distribution-If-it-is-known-that-X-i-uniform-0-1-and-let-S-X-1-X-2-Determine-the-Probability-density-function-from-S-

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