Let X denote the number of hours you study during a randomly selected school day The probability that X can take the values x. has the following form, where k is some unknown constant. `P(X=x)={0. 1 if x=0,k x if x=1 , 2k(5-x) if x=3 or 4, 0 otherwise

Let X denote the number of hours you study during a randomly selected school day The probability that X can take the values x .has the following form,where k is some unknown constant.' P(X=x)={0.1 if x=0,kx if x=12k(5-x) if x=3 or 4,0 otherwise

Let 'X' denote the number of hours you study during a randomly selected school day. The probability that 'X' can take the values of x has the following form, where k is some unknown constant. P(X=x)={{:(0.1",","if",x=0),(kx",","if",x=1" or "2),(k(5-x)",","if",x=3" or "4),(0",",,"otherwise.":} (a) Find the value of 'k'. (b) What is the probability that you study at least two hours ? Exactly two hours ? At most two hours ?

Let denote the number of fruits that are grown in a farm house in a particular day. The probability that X can take the value of x has the following form, where k is some unknown constant. P(X=x) = {(k, if x=0),(2k, if x=1),(3x, if x=2), (0, "otherwise"):} Then the value of k is

Let, X denote the number of colleges where you will apply after your results and P (X = x) denotes your probability of getting admission in x number of colleges. It is given that P(X=x)={k x,ifx=0or1 2k x,ifx=2k(5-x),ifx=3or4 0,ifx >4 where k is a positive constant. Find the value of k . Also find the probability that you will get admission in (i) exactly one college (ii) at most 2 colleges (iii) at least 2 colleges.