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 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"):} Find: (i) k (ii) the probability that you study exactly two hours, (iii) the probability that you study at most two hours.

Let X denote the no. of hours you study during a randomly selected school day. The probability that X can take the values x, has the following form, where lamda is some unknown constant. (a) Find the value of lamda (b) What is the probability that you study at least two hours ? Exactly two hours? At most two hours?

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=2,k(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.

The random variable X has a probability distribution P(X) of the following form, where k is some number : P(X) = {(k ,if x=0) , (2k ,if x=1), (3k ,if x=2), (0 otherwise) (a) Determine k. (b) Find P ( X lt 2) , P ( X le 2) , P (X ge 2 )

A random variable X takes the values 0,1,2,3,..., with prbability PX(=x)=k(x+1)((1)/(5))^x , where k is a constant, then P(X=0) is.

For what value of k is the function f(x)={(sin5x)/(3x),\ \ \ if\ x!=0,\ \ \ \ \ k ,\ \ \ if\ x=0 continuous at x=0 ?

Find the value of the constant k so that the given function is continuous at the indicated point: f(x)={((1-cos2k x)/(x^2), if x!=0 ),(8, if x=0):} at x=0

Find the value of the constant k so that the given function is continuous at the indicated point: f(x)={k(x^2+2),\ \ \ if\ xlt=0 3x+1,\ \ \ if\ x >0 at x=0 .

Determine the value of the constant k so that the function f(x)={(sin2x)/(5x),\ \ \ if\ x!=0 \ \ \ \ ,k \ \ \ if\ x=0 is continuous at x=0 .

The random variable X has a probability distribution P(X) of the following form, where k is some arbitary real number: P(X=x)={{:(k",","if "x=0), (2k",","if "x=1), (3k",","if "x=2), (0",", otherwise):} (i) Determine the value of k " " (ii) Find P(X lt 2), P(X le 2), P(X ge 2)