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Choose the correct alternative: ∫-∞∞ f(x) dx is always equal to

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प्रश्न

Choose the correct alternative: 

`int_(-oo)^oo` f(x) dx is always equal to

पर्याय

  • zero

  • one

  • E(X)

  • f(x) + 1

MCQ
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उत्तर

one

shaalaa.com
Mathematical Expectation
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Random Variable and Mathematical expectation - Exercise 6.3 [पृष्ठ १४२]

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सामाचीर कलवी Business Mathematics and Statistics [English] Class 12 TN Board
पाठ 6 Random Variable and Mathematical expectation
Exercise 6.3 | Q 17 | पृष्ठ १४२

संबंधित प्रश्‍न

For the random variable X with the given probability mass function as below, find the mean and variance.

`f(x) = {{:((4 - x)/6,  x = 1","  2","  3),(0,  "otherwise"):}`


Two balls are drawn in succession without replacement from an urn containing four red balls and three black balls. Let X be the possible outcomes drawing red balls. Find the probability mass function and mean for X


A commuter train arrives punctually at a station every half hour. Each morning, a student leaves his house to the train station. Let X denote the amount of time, in minutes, that the student waits for the train from the time he reaches the train station. It is known that the pdf of X is

`f(x) = {{:(1/30, 0 < x < 30),(0, "elsewhere"):}`
Obtain and interpret the expected value of the random variable X


Choose the correct alternative:

Four buses carrying 160 students from the same school arrive at a football stadium. The buses carry, respectively, 42, 36, 34, and 48 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying the randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on that bus. Then E(X) and E(Y) respectively are


Let X be a continuous random variable with probability density function
f(x) = `{{:(3/x^4",",  x ≥ 1),(0",",  "otherwise"):}`
Find the mean and variance of X


In investment, a man can make a profit of ₹ 5,000 with a probability of 0.62 or a loss of ₹ 8,000 with a probability of 0.38. Find the expected gain


In a business venture a man can make a profit of ₹ 2,000 with a probability of 0.4 or have a loss of ₹ 1,000 with a probability of 0.6. What is his expected, variance and standard deviation of profit?


The number of miles an automobile tire lasts before it reaches a critical point in tread wear can be represented by a p.d.f.
f(x) = `{{:(1/30 "e"^(- x/30)",",  "for"  x > 0),(0",",  "for"  x ≤ 0):}`
Find the expected number of miles (in thousands) a tire would last until it reaches the critical tread wear point


Choose the correct alternative:

Probability which explains x is equal to or less than a particular value is classified as


Choose the correct alternative: 

The distribution function F(x) is equal to


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