A student is asked to pick marbles from a bag that contains 18 marbles. 8 marbles are red, 4 are green, and 6 are black. What is the minimum number of marbles that a blindfolded student would have to draw from the bag to be certain of having at least three marbles of red color?
A Finite final consists of 50 multiple choice questions. If each question has 5 choices and 1 right answer, find the probability that a student gets an A (i.e. 45 or better) by purely guessing on each question.
Assume that when adults with smartphones are randomly selected, 48% use them in meetings or classes. If 25 adult smartphone users are randomly selected, find the probability that exactly 16 of them use their smartphones in meetings or classes.
Assume that when adults with smartphones are randomly selected, 48% use them in meetings or classes. If 25 adult smartphone users are randomly selected, find the probability that exactly 16 of them use their smartphones in meetings or classes.
Which of the following statements is correct?
a.) With a larger sample, the mean differences examined here would increase (all other parameters remaining the same).
b.) If the standard deviations of the variable "Δ anxiety TSST" in both groups were smaller than those reported here, the t-value for the mean comparison of these variables would be larger (all other parameters being equal).
c) If, in addition to male and female adolescents, adolescents of diverse genders had also been interviewed, the t-test would no longer have been applicable. i
.e.) If it turned out that some questionnaires were incorrectly scored and the mean values for perceived stress in the group of high self-compassion were greater than 27.50, this would increase the t-value for the comparison of means (all other parameters being equal ). e.
d) To compare negative and positive affect within the group of people with low self-compassion, a one-sample t-test would be used.
The joint cumulative density function of the random variables X and Y is given by:
Find the:
(i) Joint probability density function of the random variables X
and Y. [3 marks]
(ii) Marginal density function of X [3 marks]
(iii) Marginal density function of Y [3 marks]
(iv) Conditional density function of X given Y = y. [2 marks]
(v) Conditional density function of Y given X = x. [2 marks]
(vi) Are X and Y independent? [2 marks]
A customer organization that evaluates new automobiles customarily reports the
number of major defects in each car examined. Let ܺ denote the number of major
defects in a randomly selected car of a certain type. The cdf of ܺ is as follows:
= (ݔ)ܨ
ە
ۖ
ۖ
۔
ۖ
ۖ
ۓ
0 if ݔ > 0
0.06 if 0 ≤ ݔ > 1
0.19 if 1 ≤ ݔ > 2
0.39 if 2 ≤ ݔ > 3
0.67 if 3 ≤ ݔ > 4
0.92 if 4 ≤ ݔ > 5
0.97 if 5 ≤ ݔ > 6
1 if 6 ≤ ݔ
Calculate the following probabilities directly from the cdf.
a. ܲ(ܺ = 2)
b. ܲ(ܺ > 3)
c. ܲ(2 ≤ ܺ ≤ 5)
d. ܲ(2 < ܺ < 5)