Find the probabilities of events

Reference no: EM13246928

A study conducted at Duke University in the mid 1990's (Madan Paidhungat, Dept of Molecular Cancer Biology) investigated the cell growth with two types of yeast cell genes: wild and mutant cdc-1. It was postulated that the mutant gene inhibits the cell growth.

Using the results of a large experimental study researchers modeled the wild and mutant cell growth (measured by a number of isolated colonies as X₁ and X₂ respectively) under 23^o Celsius temperature and controlled environment (carbon source, richness and composition of media).

The postulated distributions were X₁ ∼ Poi(64) for the wild cells and X₂ ∼ Poi(55) for the cdc-1 mutants.

(a) Find the probabilities of events {X₁ ≤ 60} or {X₂ ≥ 60}.

(b) Find x* so that the probability of {X₁ > x*} is 0.25.

(c) Take two independent counts X₁ and X₂ from their respective distributions and find the probability that X₁ + X₂ exceeds 100. Hint: If X₁ ∼ Poi(λ₁) and X₂ ∼ Poi(λ₂) are independent, then X₁ + X₂ ∼ Poi(λ₁ + λ₂).

Reference no: EM13246928

Questions Cloud

Find out whether a solid forms when solutions : determine whether a solid forms when solutions containing the following salts are mixed. if so write the net ionic equation for the reaction. a)Na3PO4(aq) and AgNO3(aq). b)K2SO4(aq) and Na2CO3(aq). c)Pb(NO3)2(aq) and Na2CO3(aq). d)BaCl2(aq) and KO..

Explain what is the gribbs free energy : Consider the reaction of Al and Al+3 and Mg and Mg+2. If the Al+3 is 0.005 M and the Mg+2 is .40 M what is the potential energy. What is the Keq. What is the Gribbs Free Energy

Determine the entropy increase in river water : A power plant delivers energy at 880 MW using steam turbines. The steam goes into the turbines superheated at 625 K, What is the entropy increase per kilogram of the downstream river water

Explain carbon-14 is a radioactive nucleus with a half-life : Carbon-14 is a radioactive nucleus with a half-life of 5760 years. Living matter exchanges carbon with its surrounding (for example, through CO2) so that a constant level of 14C is maintained, corresponding to 15.3 decay events per minute

Find the probabilities of events : Find the probabilities of events and results of a large experimental study researchers modeled the wild and mutant cell growth

Evaluate the equilibrium constant for the reaction : Calculate the equilibrium constant for the following reaction at 298K and biological standard state: CH3CHO +NADH +H+ --> C2H5OH + NAD+ E° ?= -0.197V for the CH3CHO/ C2H5OH couple.

Calculate the net change in entropy of the system : A 2.8-kg piece of aluminum at 28.5 degrees celsius is placed in 1.0 kg of water in a Styrofoam container at room temperature (20 degrees celsius)

State chlorine gas in tap water escapes as the sample warms : explain the following observations: a)an open can of soda loses its "fizz" more quickly at room temperature than in the refrigerator. b) chlorine gas in tap water escapes as the sample warms to room temperature. c)less sugar dissolves in iced coff..

Find average distance between molecules : A container has a pressure of 4 atmospheres and is at the temperature of 200 degrees celsius, what is the average distance between molecules (assume container is a cube)

User Account

All Pages