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a workshop contains fur persons available for work on the four jobs only one person can work or anyone job the following table shows the cost of assigning each person on each job the objective only one person can work n any one job the following table shows the cost of assigning person to jobs such the total assignment cst is minimum


Four coins are tossed. Let Z be the random variable representing the number of heads that occur. Find the values of the random variable Z.


In (𝑍, +) , let 𝐻 = 𝑠𝑒𝑑 π‘œπ‘“ π‘Žπ‘™π‘™ π‘šπ‘’π‘™π‘‘π‘–π‘π‘™π‘’π‘  π‘œπ‘“ 3 and


𝐾 = 𝑠𝑒𝑑 π‘œπ‘“ π‘Žπ‘™π‘™ π‘šπ‘’π‘™π‘‘π‘–π‘π‘™π‘’π‘  π‘œπ‘“ 5.


Show that H and K are subgroups of Z . Also describe 𝐻 ∩ 𝐾

Prove the limit of π‘₯𝑛 =1/2 [π‘₯π‘›βˆ’1 + π‘₯𝑛]

How many circular permutations are there given the numbers on the clock?



Two coins are tossed. Let T be the number of tails that occur.

Construct the probability histogram.


A population consist of the value ( 1,4,3,2). Consider sample of sizes 2 that can be drawn from this population.


Find the distinct interval of length 1 containing a root or solutin of f(x) = xΒ³ - 3x + 5 using IVT

Let p and q be the propositions β€œYou can take the flight” and β€œYou buy a ticket,” respectively.



Express each of these compound propositions as an English sentence.



a) ¬p b) p∨q



c) Β¬p∧q d) q β†’ p e) Β¬q β†’Β¬p



f) Β¬p β†’Β¬ q g) p ↔ q h) Β¬q ∨(Β¬p∧ q)



Let x be a binomial random variable with n=20 and p = 0.1.


a. Find the formula for the probability distribution of x.


b. Calculate P(X≀4)


c. Calculate the mean and standard deviation of X.

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