![b) A loaded dice never lands showing the number 2, lands showing 6 with probability 1/3, and all other numbers with probability 1/6. i) Calculate the probability that 3 such loaded dice land showing the same number 4 marks] Calculate the probability that when one such loaded dice is thrown together 3 marks] ii) with a fair dice they land showing the same number. c) The mean free path of a hydrogen molecule in air is 110 nm at standard temperature and pressure. Find the probability that a hydrogen molecule has more than one collision while it travels 220 nm [5 marks] d) The probability distribution of a continuous random variable a is denoted as fax). State carefully how f(x) is to be interpreted. Write down the equation by which <x>, [5 marks] the expectation value of x, is defined in terms off(x). e) The measured voltage in an electrical circuit has a normal distribution with mean 120 V and a standard deviation 2 V. If two independent measurements are made, what is the probability that both will be between 118 V and 122 V? [5 marks]](http://img.homeworklib.com/questions/0e53a2a0-739b-11ea-83a5-af0510513a73.png?x-oss-process=image/resize,w_560)
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b) A loaded dice never lands showing the number 2, lands showing 6 with probability 1/3,...
Q3: TRUE OR FALSE You roll three fair dice -- one with seven sides (numbered 1...
Q3: TRUE OR FALSE You roll three fair dice -- one with seven sides (numbered 1 to 7), one with eight sides (numbered 1 to 8), and one with nine sides (numbered 1 to 9). X = number of dice showing odd numbers facing up. i)There are a fixed number of trials, n. 2)Each trial can be categorized as being either a success or a failure (two outcomes), and X counts the number of successes. 3)The probability of success p...
1. If two distributions have the same range, then what must be equal? a) their high...
1. If two distributions have the same range, then what must be equal? a) their high and low data values 2. In a skewed distribution, the median is preferred over the mean as a measure of the center because: a) the median is the most frequent number İfadistribution has a mean of 9 and five ofthe six data values are 6, 8, 11, 15,and18,then the missing data value is: a) 0 4. Gail received a grade of 75 on her...
Complete parts (a) and (b) below. The number of dogs per household in a small town Dogs: 0 1 2 3 4 5 Probability: 0...
Complete parts (a) and (b) below. The number of dogs per household in a small town Dogs: 0 1 2 3 4 5 Probability: 0.677 0.203 0.079 0.023 0.013 0.005 (a) Find the mean, variance, and standard deviation of the probability distribution. Find the mean of the probability distribution. μ= (Round to one decimal place as needed.)
SEED NUMBER: 3932 3.) For this problem you need to generate data so open the probability...
SEED NUMBER: 3932
3.) For this problem you need to generate data so open the probability simulator on the TI calculator and set your seed (Use last 4 digits of your GCID). Select the Roll Dice simulator and set the number of trials to 16, and the number of Sides to 12. Execute Roll and save Data to a list. PROB SIM APP Call the corresponding random variable X. Settings Trial Set: 16 Dice: 1 2 3 Sides: 6 8...
3. The probability distribution of the discrete random variable X is f(x) = 2 x 1...
3. The probability distribution of the discrete random variable X is f(x) = 2 x 1 8 x 7 8 2−x , x = 0, 1, 2. Find the mean of X. 4. The random variable X, representing the number of errors per 100 lines of software code, has the following probability distribution: x 1 2 3 5 6 f(x) 0.03 0.37 0.2 0.25 0.15 (a) Find E(X). (b) Find E(X2 ). 5. Use the distribution from Problem 4. (a)...
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Question 1 [12 + 4 =16 marks] A. Let A and B be two events such...
Question 1 [12 + 4 =16 marks] A. Let A and B be two events such that P( A) 0.6 , P(B) 0.4 and P( A B) 0.10. Calculate P( A B). Calculate P( A | B). iii. Are events A and B independent? Justify your answer. iv. Are events A and B mutually exclusive events? Justify your answer. (2 + 2 + 3 + 3 = 10 marks) B. A box contains 20 DVDs,...
The probability density function for a random variable X with a discrete uniform distribution over the integers 1, 2, 3, 4, 5, and 6 is
The probability density function for a random variable X with a discrete uniform distribution over the integers 1, 2, 3, 4, 5, and 6 is f(x) = 1/6 for x = 1, 2, 3, 4, 5, 6. What is the mean of the distribution of X? The probability density function for a random variable X with a discrete uniform distribution over the integers 1, 2, 3, 4, 5, and 6 is f(x) = 1/6 for x = 1, 2, 3, 4, 5,...
Math 6 SL Probability Distributions Practice Test Questions
Let X be normally distributed with mean 100 cm and standard deviation 5 cm.
(a) On the diagram below, shade the region representing P(X > 105).
(2)
(b) Given that P(X < d) = P(X > 105), find the value of d.
(2)
(c) Given that P(X > 105) = 0.16 (correct to two significant figures), find P(d < X < 105).
(2)
(Total 6 marks)
2. A test has five questions. To pass the test, at least three of...
Final Exam 1/13/19 Nam If two distributions have the same range, then what must be a)...
Final Exam 1/13/19 Nam If two distributions have the same range, then what must be a) their high and low data values b) the entire distributions (e) their standard deviations d) the difference between their high and low data values e) their means 1. In a skewed distribution, the median is preferred over the mean as a measure of the center because a) the median is the most frequent number b) the mean may be too heavily influenced by outliers...
1. If two distributions have the same range, then what must be equal? a) their high and low data values 2. In a skewed distribution, the median is preferred over the mean as a measure of the center because: a) the median is the most frequent number İfadistribution has a mean of 9 and five ofthe six data values are 6, 8, 11, 15,and18,then the missing data value is: a) 0 4. Gail received a grade of 75 on her...
SEED NUMBER: 3932
3.) For this problem you need to generate data so open the probability simulator on the TI calculator and set your seed (Use last 4 digits of your GCID). Select the Roll Dice simulator and set the number of trials to 16, and the number of Sides to 12. Execute Roll and save Data to a list. PROB SIM APP Call the corresponding random variable X. Settings Trial Set: 16 Dice: 1 2 3 Sides: 6 8...
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Final Exam 1/13/19 Nam If two distributions have the same range, then what must be a) their high and low data values b) the entire distributions (e) their standard deviations d) the difference between their high and low data values e) their means 1. In a skewed distribution, the median is preferred over the mean as a measure of the center because a) the median is the most frequent number b) the mean may be too heavily influenced by outliers...
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