Select Goal &
City
Select Goal
Explore
Question:
Consider the normal probability distribution function \( f(x) = \frac{4}{\sqrt{2\pi}} e^{-8(x+3)^2} \). If \( \mu \) and \( \sigma \) are the mean and standard deviation of \( f(x) \) respectively, then the ordered pair \((\mu, \sigma)\) is:
Consider the normal probability distribution function \( f(x) = \frac{4}{\sqrt{2\pi}} e^{-8(x+3)^2} \). If \( \mu \) and \( \sigma \) are the mean and standard deviation of \( f(x) \) respectively, then the ordered pair \((\mu, \sigma)\) is:
Updated On: Jul 17, 2024
- \((3, \frac{1}{4})\)
- \((-3, \frac{1}{4})\)
- \((3, 4)\)
- \((-3, 4)\)
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The correct option is (B) :\((-3, \frac{1}{4})\)
Was this answer helpful?
0
0
Questions Asked in GATE CH exam
- Methane combusts with air in a furnace according to the reaction \( \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \). The heat of reaction \( \Delta H_{\text{rxn}} \) is -880 kJ per mol of CH4 and is assumed constant. The furnace is well-insulated, and no side reactions occur. All components behave as ideal gases with a constant molar heat capacity of 44 J mol\(^{-1}\) °C\(^{-1}\). Air is composed of 20 mol% O2 and 80 mol% N2. The air-fuel mixture enters the furnace at 50°C. The methane conversion \( X \) varies with the air-to-methane mole ratio \( r \) as \( X = 1 - 0.1 e^{-2(r-r_s)} \) with \( 0.9 r_s \leq r \leq 1.1 r_s \), where \( r_s \) is the stoichiometric air-to-methane mole ratio. For \( r = 1.05 r_s \), the exit flue gas temperature in °C, rounded off to 1 decimal place, is _____.
- GATE CH - 2024
- Heat of reaction
- A solid slab of thickness \( H1 \) is initially at a uniform temperature \( T0 \). At time \( t = 0 \), the temperature of the top surface at \( y = H1 \) is increased to \( T1 \), while the bottom surface at \( y = 0 \) is maintained at \( T0 \) for \( t \geq 0 \). Assume heat transfer occurs only in the \( y \)-direction, and all thermal properties of the slab are constant. The time required for the temperature at \( y = \frac{H1}{2} \) to reach 99% of its final steady value is \( T1 \). If the thickness of the slab is doubled to \( H2 = 2H1 \), and the time required for the temperature at \( y = \frac{H2}{2} \) to reach 99% of its final steady value is \( T2 \), then \( \frac{T2}{T1} \) is .
- GATE CH - 2024
- Heat Transfer
- The temperatures of two large parallel plates of equal emissivity are 900 K and 300 K. A reflection radiation shield of low emissivity and negligible conductive resistance is placed parallelly between them. The steady-state temperature of the shield, in K, is
- GATE CH - 2024
- Heat Transfer
- Consider a vapour-liquid mixture of components A and B that obeys Raoult's law. The vapour pressure of A is half that of B. The vapour phase concentrations of A and B are 3 mol m\(^{-3}\) and 6 mol m\(^{-3}\), respectively. At equilibrium, the ratio of the liquid phase concentration of A to that of B is:
- GATE CH - 2024
- Phase equilibria
- A simple distillation column separates a binary mixture of A and B. The relative volatility of A with respect to B is 2. The steady-state composition of A in the vapour leaving the 1st, 2nd and 3rd trays in the rectifying section are 94, 90 and 85 mol%, respectively. For ideal trays and constant molal overflow, the reflux-to-distillate ratio is
- GATE CH - 2024
- Design and operation of equipment for distillation
View More Questions
SUBSCRIBE TO OUR NEWS LETTER
COLLEGE NOTIFICATIONSEXAM NOTIFICATIONSNEWS UPDATES
Download the Collegedunia app on 
© 2024 Collegedunia Web Pvt. Ltd. All Rights Reserved