A computer program requires C clock cycles (in billions) for completion, where C is a random variable uniformly distributed over {1, 2, . . . , 4}. Furthermore, this program is randomly scheduled to run over one of two computers, with equal probability. The processor of Computer 1 runs at one Gigahertz, and the processor of Computer 2 runs at two Gigahertz.

a. Compute the probability that this program needs more than 2.5 billion cycles to complete.
b. Calculate the probability that this program takes less than two seconds to execute, given that it is scheduled to run on Computer 2.
c. Find the mean and variance of the execution time of this program if it is scheduled to run on Computer 1.
d. Find the mean and variance of the execution time of this program if it is scheduled to run on Computer 2.
e. Find the (unconditioned) mean and the (unconditioned) variance of the execution time.

a) the probability that the program needs more than 2.5 billion cycles to complete is 0.5.

b) the probability that the program takes less than two seconds to execute, given that it is scheduled to run on Computer 2 is 0.75.

c) the mean and variance of the execution time of the program if it is scheduled to run on Computer 1 are 2.5 seconds and 1.25 s² respectively.

d) the mean and variance of the execution time of the program if it is scheduled to run on Computer 2 are 1.25 seconds and 0.3125 s² respectively

e) the (unconditional) Mean and (unconditional)variance of the execution time are 1.875 seconds and 0.703 s²  respectively

Step-by-step explanation:

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights