हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी वाणिज्य कक्षा १२

The time to failure in thousands of hours of an important piece of electronic equipment used in a manufactured DVD player has the density functionf(x) = e,,otherwise{2e-2x, x>00, otherwiseFind

Advertisements
Advertisements

प्रश्न

The time to failure in thousands of hours of an important piece of electronic equipment used in a manufactured DVD player has the density function
f(x) = `{{:(2"e"^(-2x)",",  x > 0),(0",",  "otherwise"):}`
Find the expected life of this piece of equipment

योग
Advertisements

उत्तर

Let X be the random variable

`"E"(x) = int_(oo)^oo x"f"(x)  "d"x`

`"E"(x) = int_0^oo x[2"e"^(2x) "d"]x`

= `2int_0^x x"e"^(-2x) "d"x`  ......`{int_0^oo x^"n""e"^(-oox)  "d"x = ("n"!)/(oo^("n" + 1))}`

= `2[(1!)/(2)]`

= `2[1/4]`

= `1/2`

∴ `"E"(x) = 1/2`

Here n = 1, `oo` = 2

shaalaa.com
Mathematical Expectation
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Random Variable and Mathematical expectation - Miscellaneous problems [पृष्ठ १४४]

APPEARS IN

सामाचीर कलवी Business Mathematics and Statistics [English] Class 12 TN Board
अध्याय 6 Random Variable and Mathematical expectation
Miscellaneous problems | Q 10 | पृष्ठ १४४

संबंधित प्रश्न

The time to failure in thousands of hours of an electronic equipment used in a manufactured computer has the density function
`f(x) = {{:(3"e"^(-3x), x > 0),(0, "eleswhere"):}`
Find the expected life of this electronic equipment


Choose the correct alternative:

Consider a game where the player tosses a six-sided fair die. If the face that comes up is 6, the player wins ₹ 36, otherwise he loses ₹ k2, where k is the face that comes up k = {1, 2, 3, 4, 5}. The expected amount to win at this game in ₹ is


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


Choose the correct alternative:

If X is a binomial random variable with I expected value 6 and variance 2.4, Then P(X = 5) is


The following table is describing about the probability mass function of the random variable X

x 3 4 5
P(x) 0.2 0.3 0.5

Find the standard deviation of x.


What are the properties of Mathematical expectation?


A person tosses a coin and is to receive ₹ 4 for a head and is to pay ₹ 2 for a tail. Find the expectation and variance of his gains


Choose the correct alternative:

Which of the following is not possible in probability distribution?


Choose the correct alternative:

E[X – E(X)] is equal to


Choose the correct alternative: 

A listing of all the outcomes of an experiment and the probability associated with each outcome is called


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×