State which of these statements is/are Correct or Incorrect and explain why. I. If S and X are events, and S is a subset of X, then P(S∩X) ≥ P(X). II. A parameter is a function of a sample. III. There are mass points that have a probability of zero. That is, if x is a mass point, then it's possible that P(X=x) = zero. IV. Given that A is normally distributed with mean of 10 and standard deviation of 5. With this, the probability that A is greater than 11 is

State which of these statements is/are Correct or Incorrect and explain why. I. If S and X are events, and S is a subset of X, then P(S∩X) ≥ P(X). II. A parameter is a function of a sample. III. There are mass points that have a probability of zero. That is, if x is a mass point, then it's possible that P(X=x) = zero. IV. Given that A is normally distributed with mean of 10 and standard deviation of 5. With this, the probability that A is greater than 11 is

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose that we have a sample space S = {E₁, E2, E3, E4, E5, E6, E7], where E₁, E2, ..., E7 denote the sample points. The following probability assignments apply: P(E₁) = 0.20, P(E₂) = 0.05, P(E3) = 0.20, P(E4) = 0.15, P(E5) = 0.25, P(E6) = 0.05, and P(E7) = 0.10. Let A = {E₁, E4, E6} B = {E2, E4, E7} C = {E2, E3, E5, E7}. Find P(AC). 0.7000 0.6000 0.3000 0.5714 O 0.4000 Question 3
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Let N be the last digit of your student number. Let X and Y be two continuous random variables that have the correlation coefficient c=0.1(N+1). Which of the following statements are true? (Wrongly ticked answers will reduce your marks in this question) a. X and Y are positively correlated. b. O c. X and Y are statistically independent. The sum of E[X] and E[Y] is equal to E[X+Y]. Od. X and Y are negatively correlated. e. The sum of Var(X) and Var(Y) is equal to Var (X+Y).
2. Customers purchase a particular make of automobile with a variety of options. The probability mass function of the number of options selected is x 7 8 9 10 11 12 13 f(x) 0.04 0.13 0.19 0.24 0.3 0.05 0.05 Consider customers that chose at most 9 options, which proportion of these cus- tomers chose 7 options? (A) 11.11% (B) 4% (C) 5.65% (D) 13% (E) 5%
b) The continuous random variable Y has the following probability density function. Pembolehubah rawak selanjar Y mempunyai fungsi ketumpatan kebarangkalian seperti berikut. Jh(3y² +2) ; -2sys2 0 ; otherwise f(y)={ 1 Show that h=- 24 i. 1 Tunjukkan bahawa h=; 24 ii. Based on the value in part (i), find the cumulative distribution function F(y). Berdasarkan nilai dalam bahagian (i), cari fungsi taburan longgokan F(y).
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2. A random variable X has a probability mass function given by: 1 0.2 a. Determine P(x) = 2 b.Find P(X<2) c. Find P(X≥ 3) X P(x) 0 0.1 2 ? 3 0.4
a. Check whether the following can be defined as probability mass function, and explain why? İ. ii. f(x) = f(x) = X 12 3x+1 50 b. Given that ƒ(x): for x = 0,1,2,3,4 k is a probability mass function for a random variable 2* that can take on the values x = 0,1,2,3, and 4. Determine the value of k - for x=0,1,2,3,4,5
1
Let (S, P) be the sample space with S = (1, 2, 3, ..., 10) and P (a) = 1/10 for all a ES. For this sample space, define the random variables X and Y by #2. X(s) = 25 and Y(s) = s a. Evaluate P (X< 10). b. Evaluate P (Y < 10).