(a) (i) Determine the constant c such that the following function for 0

MATLAB: An Introduction with Applications
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(a) (i) Determine the constant c such that the following function
f (x) =
for 0 <r <c
elsewhere
can serve as a probability density function for the random variable X.
(ii) Given the value of c found in (i), calculate P (1/2 < X < 1).
(iii) Calculate E (X).
(b) (i) Determine the constant c such that the following function
S (2r, y) = { c(a² + 4xy) for 0 < ¤ < 1, 0<y <1
elsewhere
can serve as a joint probability density for the random variables X and Y
(ii) Calculate P (X < a) for 0 <a < 1.
Transcribed Image Text:(a) (i) Determine the constant c such that the following function f (x) = for 0 <r <c elsewhere can serve as a probability density function for the random variable X. (ii) Given the value of c found in (i), calculate P (1/2 < X < 1). (iii) Calculate E (X). (b) (i) Determine the constant c such that the following function S (2r, y) = { c(a² + 4xy) for 0 < ¤ < 1, 0<y <1 elsewhere can serve as a joint probability density for the random variables X and Y (ii) Calculate P (X < a) for 0 <a < 1.
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