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Higher Study | Engineering Mathematics | Probability and Statistics

Let X and Y be two independent random variables. Which one of the relations between expectation (E), variance (Var) and covariance (Cov) given below is FALSE?
Consider a company that assembles computers. The probability of a faulty assembly of any computer is p. The company therefore subjects each computer to a testing process. This testing process gives the correct result for any computer with a probability of q. What is the probability of a computer being declared faulty?
60% of the employees of a company are college graduates. Of these, 10% are in sales. Of the employees who did not graduate from college, 80% are in sales. The probability that an employee selected at random is in sales, is:
Which type of sampling is one where only the first sample unit is selected at random and the remaining units are automatically selected in a definite sequence at equal spacing from one another. It is:
Factory A and Factory B employ 476 and 524 employees. respectively. The average weekly salary of an employee in Factory A is $34.5 whereas for an employee in Factory B it is $28.5, The standard deviation in paying the individual salary has been recorded as $5 and $4.5 for Factory A and Factory B, respectively. Which factory has greater variability in paying individual salary?
If p(x) = \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qadaGabaWdaeaafaqabeGabaaabaWdbmaalaaapaqaa8qacaWG4baa % paqaa8qacaaIXaGaaGynaaaacaGG7aGaamiEaiabg2da9iaaigdaca % GGSaGaaGOmaiaacYcacaaIZaGaaiilaiaaisdacaGGSaGaaGynaaWd % aeaapeGaaGimaiaacUdacaWGLbGaamiBaiaadohacaWGLbGaam4Dai % aadIgacaWGLbGaamOCaiaadwgaaaGaai4jaaGaay5EaaGaaiiOaiaa % dshacaWGObGaamyzaiaacckacaWGWbGaamOCaiaad+gacaWGIbGaam % yyaiaadkgacaWGPbGaamiBaiaadMgacaWG0bGaamyEaiaacckacaWG % qbGaaiiOamaacmaapaqaa8qadaWcaaWdaeaapeGaaGymaaWdaeaape % GaaGOmaaaacqGH8aapcaWGybGaeyipaWZaaSaaa8aabaWdbiaaiwda % a8aabaWdbiaaikdaaaaacaGL7bGaayzFaaaaaa!6956! \left\{ {\begin{array}{*{20}{c}} {\frac{x}{{15}};x = 1,2,3,4,5}\\ {0;elsewhere} \end{array}'} \right.\;the\;probability\;P\;\left\{ {\frac{1}{2} < X < \frac{5}{2}} \right\}\)\(\left\{\begin{matrix} \rm\frac{x}{15};&\rm x = 1,2,3,4,5 \\ 0;&\rm \text{elsewhere} \end{matrix}\right.\), the probability \(\rm P\left\{ \frac{1}{2} < X < \frac{5}{2}\right\}\) is equal to:
In the regression model ( y = a + bx) where x̅ = 2.50, y̅ = 5.50 and a = 1.50 (x̅ and y̅ denote mean of variables x and y and a is a constant), which one of the following values of parameter 'b' of the model is correct?
Consider a random process given by x(t) = A cos (2π fC t + θ), where A is a Rayleigh distributed random variable and θ is uniformly distributed in [0, 2π]. A and θ are independent. For any time t, the probability density function (PDF) of x(t) is:
A fair coin is tossed independently four times. The probability of the event “the number of times heads show up is more than the number of times tails show up" is
A probability distribution with right skew is shown in the figure The correct statement for the probability distribution is
A manufacturer knows that the condensers he makes contain on an average 1% of defectives. He packs them in boxes of 100. What is the probability that a box picked out at random will contain 4 or more faulty condensers?
The probability of student A passing an exam is 2/7 and that of B passing is 5/7. If these probabilities are independent, what is the probability that only B passes the examination
What percentage of scores falls within three standard deviations from the mean for the normal variate?
What is the probability that divisor of 1099 is a multiple of 1096 ?
In a box of 100 bulbs 30 are defective. What is the probability of getting more than 2 defective bulbs if 5 are chosen randomly from the box?
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