Using the uniform probability density function shown to the right, find the probability that the random variable X is between 1.2 and 1.8. Af(x) .5- 0- The probability is I: (Type an integer or a decimal.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![Using the uniform probability density function shown to the right, find the probability that the random variable X is between 1.2 and 1.8.
Af(x)
.5-
0+
The probability is
(Type an integer or a decimal.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffda25c89-4220-4142-ade9-5241f0c3f2f9%2F9da226a8-a8ea-4390-babf-d9119393cabe%2Fcyoo7z8_processed.png&w=3840&q=75)
![A market researcher wants to determine whether a new model of a personal computer that had been advertised on a late-night talk show had achieved more
brand-name recognition among people who watched the show regularly than among people who did not. After conducting a survey, it was found that 16% of all people
both watched the show regularly and could correctly identify the product. Also, 18% of all people regularly watched the show and 49% of all people could correctly
identify the product. Define a pair of random variables as shown below. Complete parts (a) through (c).
X= 1 if regularly watch the show
Y = 1 if product correctly identified
X = 0 otherwise
Y = 0 otherwise
a. Find the joint probability function of X and Y.
1
Y
1
(Do not round.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffda25c89-4220-4142-ade9-5241f0c3f2f9%2F9da226a8-a8ea-4390-babf-d9119393cabe%2Fa8l1sz_processed.png&w=3840&q=75)
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