1(a)Consider the random variable model with density function given by f(x)= { 2kx/45,   0≤x≤5             2k(30−x)/45 , 5≤x≤10                                  0, otherwise Compute the (i) expected value (ii) standard deviation. comment and discuss on the output of these two components with the type the random variable model defined   (b). If f (x)=ce−0.2x , if 0≤x≤10 and 0, otherwise Based on your computations below, explain and discuss the various probabilities with respect to the given exponential function. (i)deduce the constant c,

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1(a)Consider the random variable model with density function given by
f(x)= { 2kx/45,   0≤x≤5

            2k(30−x)/45 , 5≤x≤10

                                 0, otherwise

Compute the
(i) expected value
(ii) standard deviation.
comment and discuss on the output of these two components with the type the random variable model defined

 

(b). If f (x)=ce−0.2x , if 0≤x≤10 and 0, otherwise
Based on your computations below, explain and discuss the various
probabilities with respect to the given exponential function.
(i)deduce the constant c, 
(ii)compute the probabilities
(alpha) p(x≥5) 
(beta) p(x<4) 
(gamma) p(3≤x≤11)

 

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