A probability denisty function for the random variable X is given by pi=ki, where k is a constant. What value must k be if X takes on integer values between 0 and 16, inclusive? Number (Note: three decimal places is sufficient)
here for this to be valid:
must be equal to 1
=k*(0+1+2+3+4.....+16)=k*136 =1
k=1/136 =0.007
A probability denisty function for the random variable X is given by pi=ki, where k is...
ion of a random variable, X, is a nonnegative Definition 1. The probability denisty function of a random variable function fx with the property that (a) for all values x, P(X = x) = fx(x) if X is discrete and (b) for all intervals [a, b], P(a < X <b) is the area under the curve of b if X is continuous. Recall the experiement from Example 2.6-6 from last class: At 25°C, 20% of a certain type of laser...
A random variable X has a distribution with probability function f(x) = K(nx)2x for x = 0,1,2,...,n where n is a positive integer. a. Find the constant k. b. Find the expected value M(S) = E(esX) as a function of the real numbers s. Compare the values of the derivative of this function M'(0) at 0 and the expected value of a random variable having the probability function above. c. What distribution has probability function f(x)? Let X1, X2 be independent random variables both...
4. Discrete random variable is given. a) Probability distribution function is if P2 P1 Pi if if F(x) if b) formula that may be used to find mean of this random variable: if xe3]
2. Let X be a discrete random variable with the probability function given by f(2) k(x2 – 2x) + 0.2 for x = 0,1, 2, 3. (Note: all answers to the questions below must be fully evaluated.] (a) Find the value of k. (b) Find f(1.38) and F(1.38). 3. According to government data, 25% of employed women have never been married. If 20 employed women are selected at random, what is the probability that two or fewer of them have...
x A probability density function of a random variable is given by f(x) = @ ż on the interval [4, 8]. Find the expected value, the variance, and the standard deviation. The expected value is u (Round to two decimal places as needed.) The variance is Var(x)=0 (Round the final answer to two decimal places as needed. Use the expected value rounded to two decimal places. Do not round any other intermediate values.) The standard deviation is o (Round the...
4.8. Let Z be a random variable with the geometric probability mass function where 0 < π < 1. (a) Show that Z has a constant failure rate in the sense that PriZ kZk1 T for k 0, 1,.... (b) Suppose Z' is a discrete random variable whose possible values are 0, 1, and for which Pr(Z'=KZ2k} = 1-π for k 0,1,.... Show that the probability mass function for Z' is p(k).
Let X be a discrete random variable with probability mass function p(k) = 1/5, k = 1, 2, . . . , 5, zero elsewhere. (a) Find the moment generating function of X. (b) Use the moment generating function in (a) to determine the convolution of two identical probability mass functions given above. This is identical to asking the probability mass function of X + Y and where X and Y are independent and each has probability mass function given...
3 The probability density function of a random variable on the interval [9, 16] is f(x) = x. Find the following values. a. Find the expected value The expected value is (Round to two decimal places as needed.) b. Find the variance. The variance is (Round to two decimal places as needed.) c. Find the standard deviation The standard deviation is (Round to two decimal places as needed.) d. Find the probability that the random variable has a value greater...
X 1 A probability density function of a random variable is given by f(x) = 10 - a on the interval [2, 8]. Find the expected value, the variance, and the standard deviation. The expected value is u ~ (Round to two decimal places as needed.) The variance is Var(X) ~ (Round the final answer to two decimal places as needed. Use the expected value rounded to two decimal places. Do not round any other intermediate values.) The standard deviation...
The probability density of a random variable X is given in the figure below. From this density, the probability that X is between 0.76 and 1.54 is: Box 1: Enter your answer as an integer or decimal number. Examples: 3, 4, 5.5172 Enter DNE for Does Not Exist, oo for Infinity