The Joint Density Function for X, Y Is Given By p

question 53

Multiple Choice

The joint density function for x, y is given by $p ( x , y ) = \left\{ \begin{array} { c c } \frac { 1 } { 150 } e ^ { - x / 10 } e ^ { - y / 15 } & x \geq 0 , y \geq 0 \\0 & \text { otherwise }\end{array} \right.$ Write down an iterated integral to compute the probability that x + y $\le$ 10.You do not need to do the integral.

• A) \(\int _ { 0 } ^ { 10 } \int _ { 0 } ^ { 10 } \frac { 1 } { 150 } e ^ { - x / 10 } e ^ { - y / 15 } d ^ { } y d x\)
• B) \(\int _ { 0 } ^ { 10 } \int _ { 0 } ^ { 10 - x } \frac { 1 } { 150 } e ^ { - x / 10 } e ^ { - y / 15 } d x d y\)
• C) \(\int _ { 0 } ^ { 10 } \int _ { 0 } ^ { 10 - x } \frac { 1 } { 150 } e ^ { - x / 10 } e ^ { - y / 15 } d y d x\)
• D) \(\int _ { 0 } ^ { 10 } \int _ { 0 } ^ { 10 - x } \frac { 1 } { 10 } e ^ { - x / 10 } e ^ { - y / 15 } d y d ^ { 2 } x\)
• E) \(\int _ { 0 } ^ { 10 - x } \int _ { 0 } ^ { 10 } \frac { 1 } { 150 } e ^ { - x / 10 } e ^ { - y / 15 } d x d y\)

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Definitions:

Overbooked

The state of accepting more reservations or commitments than the available capacity can accommodate.

Capacity Management

The practice of balancing supply and demand by managing resources to maximize output and efficiency without overburdening production or services.

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The combination of factors that can be controlled by a company to influence consumers to purchase its products, typically identified as product, price, place, and promotion.

Consumer Demand

The desire and willingness of consumers to purchase goods and services at various price points, influencing market dynamics and pricing.