Question: Let Z N(0, 1). If we define X = e Z+ , then we say that X has a log-normal distribution with parameters

Let Z ∼ N(0, 1). If we define X = eσZ+μ, then we say that X has a log-normal distribution with parameters μ and σ, and we write X ∼ LogNormal(μ, σ).

a. If X ∼ LogNormal(μ,σ), find the CDF of X in terms of the Φ function.

b. Find EX and Var(X).

Step by Step Solution

★★★★★

3.27 Rating (156 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a To find the cumulative distribution function CDF of X when X follows a lognormal distribution Log ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Introduction To Probability Statistics Questions!

Q:

A depreciation schedule for semi-trucks of Ichiro Manufacturing Company was requested by your auditor soon after December 31, 2013, showing the additions, retirements, 2 depreciation, and other data...

Q:

The following balances were extracted from the accounting records of Brakes Ltd for the financial year ended 28 February 2022: Revenue...

Q:

The distribution of X, the life of a transistor, in hours, is approximated by a triangular distribution as follows: (a) What is the value of a? (b) Find the expected value of the life of transistors....

Q:

Let X1 and X2 have independent gamma distributions with parameters α, θ and β, θ, respectively. Let W = X1/(X1 + X2). Use a method similar to that...

Q:

Provide solutions to the attached questions below. ) Determine the inverse demand function. 0) Determine the vertical intercept of the inverse demand function. )Determine the horizontal intercept of...

Q:

2. At this point, we can analyze (stability, steady-state gain, sinusoidal steady-state gains, time-constant, etc.) of first-order, linear dynamical systems. We previously analyzed a Ist-order...

Q:

solve the following attachments. Question 1 There are 10,000 identical individuals in the market for commodity X, each with a demand function given by Qodx = 12 - 2Px, and 1000 identical producers of...

Q:

Simple linear regression is a statistical method that allows us to summarize and study relationships between two continuous (quantitative) variables: One variable, denoted X, is regarded as the...

Q:

Provide step by step solutions to the following questions. Question 1 There are 10,000 identical individuals in the market for commodity X, each with a demand function given by Qodx = 12 - 2Px, and...

Q:

solve the following attachments. Question 1 There are 10,000 identical individuals in the market for commodity X, each with a demand function given by Qodx = 12 - 2Px, and 1000 identical producers of...

Q:

Provide solutions for the questions attached below. Use the willingness-to-pay information about the buyers (Ariel, Bridget, and Connie) and the willingness-to-accept information about the sellers...

Q:

Park Corporation acquired the voting stock of Sequoia Company on January 1, 2020 for $25 million in cash and stock. At the date of acquisition, Sequoia's book value totaled $3 million, consisting of...

Q:

In Fig. 4-41, a ball is launched with a velocity of magnitude 10.0m/s, at an angle of 50.0 o to the horizontal. The launch point is at the base of a ramp of horizontal length d 1 = 6.00 m and height...

Q:

10. Surface hardening is an example of (a) Production by application of machine tool, ( ) (b) Production by disintegration, ( ) (c) Production by Integration, ( ) ( d) Production by Service. ( )

Q:

464 Using a single OP AMP, design a circuit with inputs v1 and v2 and an output vO = v2 5v1. The input resistance seen by each input should be greater than 1 k.

Q:

Large maps are printed on a plotter and rolled up. The supervisor randomly selects 12 printed maps and unfolds a part of each map to verify the quality of the printing. List one condition under which...

Q:

An inspector examines every twentieth piece coming off an assembly line. List some of the conditions under which this method of sampling might not yield a random sample.

Q:

A bioengineering company manufactures a device for externally measuring blood flow. Measurements of the electrical output (milliwatts) on a sample of 16 units yields the data plotted in Figure 9.5....

Q:

(1) A cash dividend of $0.50 per share is declared, but not distributed 2) A 10 percent stock dividend is declared and issued (3) 500 shares of treasury stock are purchased (4) Additional shares of...

Q:

A department uses the FIFO method of process costing. All direct materials are added at the beginning of the process. This department has the following data for this month. 176 units in beginning WIP...

Q:

When Danny withdrew from John, Daniel, Harry, and Danny LLP, he was paid $75,000, although his capital account balance was only $60,000. The four partners shared net income and losses equally. The...